优化算子分裂在麦克斯韦方程组的数值积分方法</t我tle> <link rel="preload stylesheet" as="style" type="text/css" href="https://cdn.bibblio.org/rcm/4.28.0/bib-related-content.min.css"> <link rel="preload" href="https://static.hindawi.com/new/next_assets/2023-08-03-0017a694320dbe69a559e8120be98c/_next/static/css/b2661f2cd4bd618b.css" as="style"> <link rel="stylesheet" href="https://static.hindawi.com/new/next_assets/2023-08-03-0017a694320dbe69a559e8120be98c/_next/static/css/b2661f2cd4bd618b.css" data-n-g=""> <style id="__jsx-903e4b2e5d3241e4">div#__next{display:-webkit-box;display:-webkit-flex;display:-moz-box;display:-ms-flexbox;display:flex;min-height:100vh;-webkit-box-orient:vertical;-webkit-box-direction:normal;-webkit-flex-direction:column;-moz-box-orient:vertical;-moz-box-direction:normal;-ms-flex-direction:column;flex-direction:column}</style> </head> <body> <div id="__next"> <section class="ant-layout"> <div> <header class="ant-layout-header"> <div class="header__width-wrapper"> <div 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class="articleHeader"> <div class="articleHeader__specialIssue"> <span class="articleHeader__specialIssue_tag">特殊的问题</年代p一个n> <h2 class="articleHeader__specialIssue_title">高性能计算和工程在电磁学中的应用</h2> <a href="//www.newsama.com/journals/ijap/si/568341/" class="articleHeader__specialIssue_url" target="_blank" rel="noreferrer">把这个特殊的问题</一个> </div> <strong>研究文章|<!- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -- - - - - - - - - -- - - - - -- - - - - ->开放获取</年代trong> <div class="articleHeader__meta"> <span>体积<!- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -- - - - - - - - - -- - - - - -- - - - - ->2012年<!- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -- - - - - - - - - -- - - - - -- - - - - ->|</年代p一个n> <span>文章的ID<!- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -- - - - - - - - - -- - - - - -- - - - - ->956431年<!- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -- - - - - - - - - -- - - - - -- - - - - ->|</年代p一个n> <span class="articleHeader__meta_doiLink"><a href="https://doi.org/10.1155/2012/956431" aria-label="Doi-link" target="_blank" rel="noreferrer">https://doi.org/10.1155/2012/956431</一个></span> </div> <div class="simpleShowMore"> <button class="simpleShowMore__button">显示引用</button> </div> <h1 class="articleHeader__title">优化算子分裂在麦克斯韦方程组的数值积分方法</h1> <div class="articleHeader__authors"> <span class="articleHeader__authors_author"><strong>z . x黄</年代trong><a href="//www.newsama.com/cdn-cgi/l/email-protection" aria-label="Mail Option"><span role="img" class="anticon"> <svg version="1.0" xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" viewbox="0 0 1401 1101"> <path fill="#6ba439" d="M132.5 2.1C101.4 6 71.1 20.5 48.3 42.4c-22.7 21.7-37.5 48.3-44.6 80l-2.2 10.1v837l2.2 10.1c6.7 30 19.3 53.9 39.8 75.3 23.3 24.3 56.4 40.9 90 45 12.8 1.6 1122.2 1.6 1135 0 38.9-4.8 75.9-25.6 100-56.4 15-19.3 24.2-39 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- -- - - - - ->,<年代up>2</年代up></span> <span class="articleHeader__authors_author">和<!- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -- - - - - - - - - -- - - - - -- - - - - ->b .吴<年代up>1</年代up></span> </div> <div class="simpleShowMore"> <button class="simpleShowMore__button">显示更多</button> </div> <div class="articleHeader__academicEditor"> <strong>学术编辑器:</年代trong> <span>宁元</年代p一个n> </div> <div class="articleHeader__timeline"> <div class="articleHeader__timeline_item "> <strong>收到了</年代trong> <span>2011年3月11日</年代p一个n> </div> <div class="articleHeader__timeline_item "> <strong>接受</年代trong> <span>2011年4月27日</年代p一个n> </div> <div class="articleHeader__timeline_item articleHeader__timeline_item_sticky"> <strong>发表</年代trong> <span>06年7月2011年</年代p一个n> </div> </div> </div> <div class="articleBody"> <div class="xml-content"> <h4 class="header" id="abstract">文摘</h4> <p>优化算子分裂方法时域麦克斯韦方程组的数值积分计算电磁学(CEM)首次提出。方法是基于麦克斯韦方程的时域演化算子分裂成suboperators,和对应的时间系数是通过减少截断术语的规范降到最低。总体介绍了高阶交错有限差分离散化在空间域三维卷曲操作符。详细的计划和明确的迭代公式。此外,新的高阶Pade逼近采用改进的效率提出了方法。理论证明的稳定性也包括在内。数值结果给出了演示方案的有效性和效率。发现优化方案与粗网格离散和大型Courant-Friedrichs-Lewy (CFL)数量可以获得满意的数值结果,进而被证明是一种很有前途的方法,具有精度高、低计算资源和设施的大型域和长期的模拟。此外,由于通用性,我们的优化方案可以扩展到其他科学和工程领域。</p> <span class="end-abs"></span> <h4 id="introduction">1。介绍</h4> <p>应用时域有限差分(2,2))方法(<一个href="#B1">1</一个>,<一个href="#B2">2</一个>)已被广泛用于模拟瞬态电磁问题的解决方案涉及到微波结构的分析和设计,许多其他工程应用和电磁波传播的各种媒体。尽管它很简单和建模功能强大;然而,FDTD(2, 2)计算非常密集,由于它的两个固有的物理约束,一个数值色散和另一个的数值稳定性。这些限制一直让它极大的兴趣提高FDTD(2, 2)效率的方案,使研究人员开发各种新方案。</p> <p>为了提高数值色散,一些高阶空间提出了策略。例如,方提出了高阶FDTD(4, 4)法(<一个href="#B3">3</一个>]。然而,该方法难以处理材料界面建模复杂的三维物体。另一种方法是交错FDTD(2、4)方法(<一个href="#B4">4</一个>- - - - - -<一个href="#B6">6</一个>]。然而,该方法必须设置低Courant-Friedrichs-Levy (CFL)获得高阶数数值精度。为了进一步探索有效的电磁仿真优化方法,新的改进策略的时间称为高阶龙格-库塔(实际)方法引入<一个href="#B7">7</一个>,<一个href="#B8">8</一个>]。然而,方法是耗散和需要大量的记忆。其它替代方法是交替方向隐式有限差分(ADI-FDTD)算法(<一个href="#B9">9</一个>,<一个href="#B10">10</一个>]。虽然可以节省CPU时间由于无条件稳定,不受欢迎的数值精度和分散采用高CFL数会发生一次。另一个系统的方法来解决时变麦克斯韦方程组数值无条件稳定的方案提出了和发达<一个href="#B11">11</一个>]。方法的基本思想是采用Lie-Trotter-Suzuki产品公式近似时间演化算符。所示(<一个href="#B12">12</一个>),大多数这些方法可以被看作是特殊情况的time-operator-splitting原时间演化算符方法分为suboperators。有两个原因。首先,许多这样的suboperators很简单,容易实现。其次,分割方法可以保持原系统的重要数学和物理性质。现在算子分裂的方法已经广泛使用,考虑到各种应用程序在科学和工程技术的发展为解决线性方程中出现油藏模拟,天体物理,生物工程应用程序建模而且海啸。</p> <p>本文特别,我们考虑优化算子分裂方法时变麦克斯韦方程组的数值解。节<一个href="#sec2">2</一个>,时域麦克斯韦方程写成一个时间演化矩阵算子的形式。新颖的方法,提出了改进的效率基于分裂成suboperator时间演化算符,和最优时间系数是通过减少截断术语的规范降到最低。总体介绍了高阶交错有限差分离散化空间域的三维卷曲运营商。并给出了明确的离散公式<一个href="#sec3">3</一个>。新的高阶Pade逼近和稳定性分析也包括在内。部分<一个href="#sec4">4</一个>给出了数值例子,结论部分<一个href="#sec5">5</一个>。</p> <h4 id="general-formulations-of-splitting-schemes">2。分割方案的一般公式</h4> <h5 id="sec2.1">2.1。时域麦克斯韦方程的唯一解矩阵形式</h5> <p>麦克斯韦方程在一个各向同性介质可以重写一个矩阵形式<年代p一个nclass="equation" id="EEq1"> <svg height="107.45" id="M1" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 107.45" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,107.45)"> <g transform="translate(72,13.96)"> <text transform="matrix(1,0,0,-1,143.94,56.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <g> <path d="m 141.98,52.73 10.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,141.98,40.85)"> <tspan style="font-size: 12.50px; " x="13.58" y="0.98000002"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="23.690001" y="-20.610001"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="24.379999" y="1.86"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="33.41" y="0.98000002"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="100.93" y="0.98000002"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="111.03" y="-20.610001"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="111.72" y="1.86"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="120.76" y="0.98000002"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="132.94" y="-8.75"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="-51.509998" y="48.400002"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="46.990002" y="-8.75"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="59.017887" y="-8.75"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="63.181385" y="-8.75"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="74.984215" y="-8.75"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="86.336945" y="-8.75"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="94.676445" y="-8.75"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="-76.050003" y="38.66"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="-63.559502" y="38.66"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="-41.41" y="27.889999"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="-32.845444" y="27.889999"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,116.75,17.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,127.62,12.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,134.96,17.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,140.04,12.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,144.9,9.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,155.75,12.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="8.5645552" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,171.93,17.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,182.8,12.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="-68.18" y="22.459999"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,120.87,-12.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ×</t年代p一个n> <tspan style="font-size: 8.75px; " x="9.9772797" y="0"> 3</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,163.24,-9.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,169.49,-12.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ×</t年代p一个n> <tspan style="font-size: 8.75px; " x="9.9772797" y="0"> 3</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,191.83,-7.55)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="61.169998" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="73.690002" y="-22.68"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="12.18" y="-9.7399998"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="37.311031" y="-9.7399998"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="49.126366" y="-9.7399998"> =</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,271.78,12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ×</t年代p一个n> <tspan style="font-size: 8.75px; " x="9.9772797" y="0"> 3</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,305.76,15.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,312.01,12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ×</t年代p一个n> <tspan style="font-size: 8.75px; " x="9.9772797" y="0"> 3</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,263.1,-9.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,269.15,-4.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,280.02,-9.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="15.0036" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="23.568155" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,309.64,-4.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,320.51,-9.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="7.3392611" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,332.72,-12.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,337.59,-7.55)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="12.19" y="-9.7399998"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="136.53" y="-33.439999"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="140.6935" y="-33.439999"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="146.94499" y="-33.439999"> )</t年代p一个n> </text> </g> </g> </svg></span>在哪里<年代vg height="9.6750002" id="M2" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>和<年代vg height="7.1875" id="M3" style="vertical-align:-0.13794pt;width:7.6875px;" version="1.1" viewbox="0 0 7.6875 7.1875" width="7.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1875)"> <g transform="translate(72,-66.25)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>磁导率和介电常数,<年代vg height="6.9875002" id="M4" style="vertical-align:-0.13794pt;width:9.3000002px;" version="1.1" viewbox="0 0 9.3000002 6.9875002" width="9.3000002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,6.9875)"> <g transform="translate(72,-66.41)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>和<年代vg height="11.7" id="M5" style="vertical-align:-0.13794pt;width:15.6375px;" version="1.1" viewbox="0 0 15.6375 11.7" width="15.6375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.7)"> <g transform="translate(72,-62.64)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-64.61,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n> </text> </g> </g> </svg>电和磁导率,<年代vg height="15.0625" id="M6" style="vertical-align:-3.35449pt;width:26.5px;" version="1.1" viewbox="0 0 26.5 15.0625" width="26.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.0625)"> <g transform="translate(72,-59.95)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-65.7,60.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ×</t年代p一个n> <tspan style="font-size: 8.75px; " x="9.9772797" y="0"> 3</t年代p一个n> </text> </g> </g> </svg>和<年代vg height="14.75" id="M7" style="vertical-align:-3.25793pt;width:12.3px;" version="1.1" viewbox="0 0 12.3 14.75" width="12.3" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-67.09,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n> </text> </g> </g> </svg>是<年代vg height="11.075" id="M8" style="vertical-align:-0.3135pt;width:32.700001px;" version="1.1" viewbox="0 0 32.700001 11.075" width="32.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.075)"> <g transform="translate(72,-63.14)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 3</t年代p一个n> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> ×</t年代p一个n> <tspan style="font-size: 12.50px; " x="19.804752" y="0"> 3</t年代p一个n> </text> </g> </g> </svg>零矩阵和单位矩阵,<年代vg height="10.6875" id="M9" style="vertical-align:-0.0pt;width:11.4125px;" version="1.1" viewbox="0 0 11.4125 10.6875" width="11.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6875)"> <g transform="translate(72,-63.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>是<年代vg height="11.075" id="M10" style="vertical-align:-0.3135pt;width:32.700001px;" version="1.1" viewbox="0 0 32.700001 11.075" width="32.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.075)"> <g transform="translate(72,-63.14)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 3</t年代p一个n> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> ×</t年代p一个n> <tspan style="font-size: 12.50px; " x="19.804752" y="0"> 3</t年代p一个n> </text> </g> </g> </svg>矩阵表示三维卷曲算子。方程(<一个href="#EEq1">1</一个>)可以在下列紧凑的形式<年代p一个nclass="equation" id="EEq3"> <svg height="30.887501" id="M11" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 30.887501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,30.8875)"> <g transform="translate(72,-47.29)"> <text transform="matrix(1,0,0,-1,175.02,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="6.6515961" y="0"> </t年代p一个n> </text> <g> <path d="m 175.02,59.37 14.99,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,177.23,47.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="6.6515961" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="17.450001" y="-8.7600002"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="29.477886" y="-8.7600002"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="37.817387" y="-8.7600002"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="48.244888" y="-8.7600002"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="52.408386" y="-8.7600002"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="56.321827" y="-8.7600002"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="62.560825" y="-8.7600002"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="296.89001" y="-8.7600002"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="301.0535" y="-8.7600002"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="307.30499" y="-8.7600002"> )</t年代p一个n> </text> </g> </g> </svg></span>在这里,<年代vg height="16.2875" id="M12" style="vertical-align:-2.21957pt;width:123.7375px;" version="1.1" viewbox="0 0 123.7375 16.2875" width="123.7375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2875)"> <g transform="translate(72,-58.97)"> <text transform="matrix(1,0,0,-1,-71.95,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.503" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="16.416439" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="24.043268" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="36.083656" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="40.247158" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="49.974491" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="54.137989" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="58.05143" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="62.214928" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="67.42868" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="75.768181" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="79.931679" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="83.845116" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="88.008614" y="0"> ]</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,20.23,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>是完整的电磁场变量。虽然只写明确时间依赖性,另外这些数量取决于空间,但符号为简单起见,我们将省略的空间相关性。如果一个初始配置<b>Z (0)</b>提供独特的解决方案(<一个href="#EEq3">2</一个>)可以表示为<年代p一个nclass="equation" id="EEq4"> <svg height="18.612499" id="M13" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 18.612499" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.6125)"> <g transform="translate(72,-57.11)"> <text transform="matrix(1,0,0,-1,119.38,60.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="14.578498" y="0"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="23.605663" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="27.519102" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="35.158436" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="47.198826" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,172.15,65.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="5.837584" y="0"> Δ</t年代p一个n> <tspan style="font-size: 8.75px; " x="12.156528" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,187.54,60.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="14.578498" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="20.829998" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="28.469332" y="0"> ≡</t年代p一个n> <tspan style="font-size: 12.50px; " x="40.50972" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,233.62,65.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="9.2333603" y="0"> +</t年代p一个n> <tspan style="font-size: 8.75px; " x="15.22848" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="21.066065" y="0"> )</t年代p一个n> <tspan style="font-size: 8.75px; " x="23.98048" y="0"> Δ</t年代p一个n> <tspan style="font-size: 8.75px; " x="30.299423" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,267.16,60.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="14.578498" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="20.829998" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="27.081497" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="206.96001" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="211.1235" y="0"> 3</t年代p一个n> <tspan style="font-size: 12.50px; " x="217.375" y="0"> )</t年代p一个n> </text> </g> </g> </svg></span>在哪里<年代vg height="10.8" id="M14" style="vertical-align:-0.11285pt;width:16.299999px;" version="1.1" viewbox="0 0 16.299999 10.8" width="16.299999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8)"> <g transform="translate(72,-63.36)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代p一个n> </text> </g> </g> </svg>表示时间步和操作员<年代vg height="11.55" id="M15" style="vertical-align:-0.51414pt;width:69.300003px;" version="1.1" viewbox="0 0 69.300003 11.55" width="69.300003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.55)"> <g transform="translate(72,-62.76)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="23.843222" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="35.646053" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="46.986275" y="0"> </t年代p一个n> </text> </g> </g> </svg>被分成两个suboperators。这种分裂的意义将在下面被理解。</p> <h5 id="sec2.2">2.2。分裂指数在时域传播算子的方法</h5> <p>注意,解决方案(<一个href="#EEq4">3</一个>)很正式,因为指数宣传者<年代vg height="13.9375" id="M16" style="vertical-align:-0.13794pt;width:26.325001px;" version="1.1" viewbox="0 0 26.325001 13.9375" width="26.325001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.9375)"> <g transform="translate(72,-60.85)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-66.39,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="5.837584" y="0"> Δ</t年代p一个n> <tspan style="font-size: 8.75px; " x="12.156528" y="0"> </t年代p一个n> </text> </g> </g> </svg>不允许评估到底在任何给定的<年代vg height="10.8" id="M17" style="vertical-align:-0.11285pt;width:16.299999px;" version="1.1" viewbox="0 0 16.299999 10.8" width="16.299999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8)"> <g transform="translate(72,-63.36)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代p一个n> </text> </g> </g> </svg>。然而,在足够小的值<年代vg height="10.8" id="M18" style="vertical-align:-0.11285pt;width:16.299999px;" version="1.1" viewbox="0 0 16.299999 10.8" width="16.299999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8)"> <g transform="translate(72,-63.36)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代p一个n> </text> </g> </g> </svg>,总传播算子可以分割使用的公式<年代p一个nclass="equation" id="EEq5"> <svg height="48.349998" id="M19" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.349998" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.35)"> <g transform="translate(72,-33.32)"> <text transform="matrix(1,0,0,-1,108.26,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,113.83,54.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Δ</t年代p一个n> <tspan style="font-size: 8.75px; " x="6.318944" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="9.05832" y="0"> (</t年代p一个n> <tspan style="font-size: 8.75px; " x="11.972736" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="18.291679" y="0"> +</t年代p一个n> <tspan style="font-size: 8.75px; " x="24.2868" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="30.124384" y="0"> )</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,150.84,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,169.28,65.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,162.87,43.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,165.81,35.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="2.7831359" y="0"> =</t年代p一个n> <tspan style="font-size: 8.75px; " x="8.7782564" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,181.9,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,187.46,54.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="5.837584" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,197.96,52.48)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,200.57,54.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Δ</t年代p一个n> <tspan style="font-size: 8.75px; " x="6.318944" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,210.13,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,215.69,54.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="6.318944" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,225.64,52.48)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,228.25,54.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Δ</t年代p一个n> <tspan style="font-size: 8.75px; " x="6.318944" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,240.59,49.67)"> <tspan style="font-size: 12.50px; " x="22.83" y="2.52"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="28.68" y="0"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="37.707165" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,282.21,54.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> +</t年代p一个n> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,297.43,47.15)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="7.9299998" y="-2.52"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="176.69" y="-2.52"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="180.8535" y="-2.52"> 4</t年代p一个n> <tspan style="font-size: 12.50px; " x="187.105" y="-2.52"> )</t年代p一个n> </text> </g> </g> </svg></span>系数<年代vg height="11.0375" id="M20" style="vertical-align:-3.22282pt;width:10.925px;" version="1.1" viewbox="0 0 10.925 11.0375" width="10.925" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0375)"> <g transform="translate(72,-63.17)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-66.76,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>和<年代vg height="14.5875" id="M21" style="vertical-align:-3.22282pt;width:12.7625px;" version="1.1" viewbox="0 0 12.7625 14.5875" width="12.7625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5875)"> <g transform="translate(72,-60.33)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-65.3,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>在这个公式应该选择以这种方式提供最高的价值<年代vg height="7.1374998" id="M22" style="vertical-align:-0.10033pt;width:7.8874998px;" version="1.1" viewbox="0 0 7.8874998 7.1374998" width="7.8874998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>在一个给定的整数<年代vg height="7.1374998" id="M23" style="vertical-align:-0.10033pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 7.1374998" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>。在这里<年代vg height="7.1374998" id="M24" style="vertical-align:-0.10033pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 7.1374998" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>塔板数需要在每一个整数时间步,然后呢<年代vg height="7.1374998" id="M25" style="vertical-align:-0.10033pt;width:7.8874998px;" version="1.1" viewbox="0 0 7.8874998 7.1374998" width="7.8874998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>是近似的顺序。上面的分裂的主要优势是time-reversibility<年代vg height="13.675" id="M26" style="vertical-align:-2.21957pt;width:111.55px;" version="1.1" viewbox="0 0 111.55 13.675" width="111.55" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.675)"> <g transform="translate(72,-61.06)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ψ</t年代p一个n> <tspan style="font-size: 12.50px; " x="9.3272381" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="13.490737" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="22.055292" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="25.968731" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="30.132231" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="38.471729" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="42.635231" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="46.548668" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="54.175499" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="66.215889" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="74.555389" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="78.718887" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="84.97039" y="0"> )</t年代p一个n> </text> </g> </g> </svg>的解决方案(以下属性<年代vg height="16.9625" id="M27" style="vertical-align:-2.21957pt;width:97.724998px;" version="1.1" viewbox="0 0 97.724998 16.9625" width="97.724998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.9625)"> <g transform="translate(72,-58.43)"> <text transform="matrix(1,0,0,-1,-71.95,60.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ψ</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-62.62,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-51.75,60.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="15.703768" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="27.744158" y="0"> Ψ</t年代p一个n> <tspan style="font-size: 12.50px; " x="37.071396" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="41.234894" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="49.79945" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="53.712887" y="0"> )</t年代p一个n> </text> </g> </g> </svg>的时间演化算符<年代vg height="16.5375" id="M28" style="vertical-align:-2.21957pt;width:75.1875px;" version="1.1" viewbox="0 0 75.1875 16.5375" width="75.1875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5375)"> <g transform="translate(72,-58.77)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ψ</t年代p一个n> <tspan style="font-size: 12.50px; " x="9.3272381" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="13.490737" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="17.404177" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="29.207008" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="45.410896" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-20.97,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="5.837584" y="0"> </t年代p一个n> </text> </g> </g> </svg>)也可以复制征收额外的时间可逆限制系数,即<年代vg height="11.375" id="M29" style="vertical-align:-3.49493pt;width:69.137497px;" version="1.1" viewbox="0 0 69.137497 11.375" width="69.137497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.375)"> <g transform="translate(72,-62.9)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-66.76,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-59.83,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-42.61,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="6.2139201" y="0"> −</t年代p一个n> <tspan style="font-size: 8.75px; " x="12.20904" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="14.992176" y="0"> +</t年代p一个n> <tspan style="font-size: 8.75px; " x="20.987295" y="0"> 1</t年代p一个n> </text> </g> </g> </svg>,<年代vg height="14.5875" id="M30" style="vertical-align:-3.22282pt;width:62.650002px;" version="1.1" viewbox="0 0 62.650002 14.5875" width="62.650002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5875)"> <g transform="translate(72,-60.33)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-65.3,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-58.37,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="14.115887" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-37.6,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="6.2139201" y="0"> −</t年代p一个n> <tspan style="font-size: 8.75px; " x="12.20904" y="0"> </t年代p一个n> </text> </g> </g> </svg>与<年代vg height="14.6875" id="M31" style="vertical-align:-3.20526pt;width:44.037498px;" version="1.1" viewbox="0 0 44.037498 14.6875" width="44.037498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6875)"> <g transform="translate(72,-60.25)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-65.3,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-55.11,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代p一个n> </text> </g> </g> </svg>。还要注意分裂方法相当的一般构建数值集成商任意命令<年代vg height="7.1374998" id="M32" style="vertical-align:-0.10033pt;width:7.8874998px;" version="1.1" viewbox="0 0 7.8874998 7.1374998" width="7.8874998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>与<年代vg height="7.1374998" id="M33" style="vertical-align:-0.10033pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 7.1374998" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>阶段。但是我们不能选择阶段<年代vg height="7.1374998" id="M34" style="vertical-align:-0.10033pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 7.1374998" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>太大,因为这会导致一个太大的数,即<年代vg height="10.8125" id="M35" style="vertical-align:-0.10033pt;width:36.6875px;" version="1.1" viewbox="0 0 36.6875 10.8125" width="36.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8125)"> <g transform="translate(72,-63.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="11.652796" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> 1</t年代p一个n> </text> </g> </g> </svg>每个时间步,昂贵的力量。在这篇文章中,特别是,我们选择<年代vg height="11.1" id="M36" style="vertical-align:-0.17555pt;width:38.424999px;" version="1.1" viewbox="0 0 38.424999 11.1" width="38.424999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.1)"> <g transform="translate(72,-63.12)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="12.340461" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="24.38085" y="0"> 5</t年代p一个n> </text> </g> </g> </svg>和减少截断误差<年代vg height="16.674999" id="M37" style="vertical-align:-2.21957pt;width:44.237499px;" version="1.1" viewbox="0 0 44.237499 16.674999" width="44.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.675)"> <g transform="translate(72,-58.66)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="9.1521959" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="13.315695" y="0"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="22.342861" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-45.69,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-40.82,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n> </text> </g> </g> </svg>明显有点额外的计算成本。</p> <p>为<年代vg height="11.1" id="M38" style="vertical-align:-0.17555pt;width:38.424999px;" version="1.1" viewbox="0 0 38.424999 11.1" width="38.424999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.1)"> <g transform="translate(72,-63.12)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="12.340461" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="24.38085" y="0"> 5</t年代p一个n> </text> </g> </g> </svg><i>,</我>扩展的分割结果可以用形式表示<年代p一个nclass="equation" id="EEq6"> <svg height="49.299999" id="M39" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 49.299999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,49.3)"> <g transform="translate(72,-32.56)"> <text transform="matrix(1,0,0,-1,50.85,60.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,56.42,65.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Δ</t年代p一个n> <tspan style="font-size: 8.75px; " x="6.318944" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="9.05832" y="0"> (</t年代p一个n> <tspan style="font-size: 8.75px; " x="11.972736" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="18.291679" y="0"> +</t年代p一个n> <tspan style="font-size: 8.75px; " x="24.2868" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="30.124384" y="0"> )</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,93.43,60.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,111.03,65.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="6.318944" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,120.98,63.72)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,124.61,65.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Δ</t年代p一个n> <tspan style="font-size: 8.75px; " x="6.318944" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,134.16,60.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,139.73,65.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="5.837584" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,150.22,63.72)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,153.84,65.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Δ</t年代p一个n> <tspan style="font-size: 8.75px; " x="6.318944" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,163.4,60.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,168.96,65.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="6.318944" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,178.92,63.72)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,182.54,65.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Δ</t年代p一个n> <tspan style="font-size: 8.75px; " x="6.318944" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,192.1,60.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,197.66,65.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="5.837584" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,208.15,63.72)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,211.78,65.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Δ</t年代p一个n> <tspan style="font-size: 8.75px; " x="6.318944" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,221.33,60.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,226.9,65.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="6.318944" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,236.85,63.72)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 3</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,240.47,65.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Δ</t年代p一个n> <tspan style="font-size: 8.75px; " x="6.318944" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,250.03,60.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,255.59,65.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="5.837584" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,266.09,63.72)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,269.71,65.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Δ</t年代p一个n> <tspan style="font-size: 8.75px; " x="6.318944" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,279.27,60.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,284.83,65.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="6.318944" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,294.78,63.72)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,298.41,65.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Δ</t年代p一个n> <tspan style="font-size: 8.75px; " x="6.318944" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,307.96,60.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,313.53,65.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="5.837584" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,324.02,63.72)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,327.64,65.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Δ</t年代p一个n> <tspan style="font-size: 8.75px; " x="6.318944" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,337.2,60.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,342.77,65.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="6.318944" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,352.72,63.72)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,356.34,65.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Δ</t年代p一个n> <tspan style="font-size: 8.75px; " x="6.318944" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,102.7,37.17)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> Υ</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,123.07,34.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,127.94,37.17)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,140.88,42.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,148.53,37.17)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> Υ</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,168.9,34.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,173.78,37.17)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,186.72,42.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,194.37,37.17)"> <tspan style="font-size: 12.50px; " x="22.83" y="2.51"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="28.68" y="0"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="37.707165" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,235.99,42.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 7</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,240.87,34.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="7.9299998" y="-2.51"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="233.25" y="-14.49"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="237.4135" y="-14.49"> 5</t年代p一个n> <tspan style="font-size: 12.50px; " x="243.66499" y="-14.49"> )</t年代p一个n> </text> </g> </g> </svg></span>还请注意,可以计算的分布函数分析如下:<年代p一个nclass="equation" id="EEq7"> <svg height="140.9875" id="M40" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 140.9875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,140.9875)"> <g transform="translate(72,40.79)"> <text transform="matrix(1,0,0,-1,63.75,45.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,69.32,50.02)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="6.318944" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,79.27,47.83)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,81.88,50.02)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Δ</t年代p一个n> <tspan style="font-size: 8.75px; " x="6.318944" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,94.91,45.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.04" y="-12.94"> ⎛</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.04" y="-2.1900001"> ⎜</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.04" y="8.5699997"> ⎜</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.04" y="19.26"> ⎝</t年代p一个n> <tspan style="font-size: 12.50px; " x="39.889999" y="1.79"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="49.259998" y="-5.54"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="17.66" y="-5.54"> e</t年代p一个n> <tspan style="font-size: 12.50px; " x="23.211332" y="-5.54"> x</t年代p一个n> <tspan style="font-size: 12.50px; " x="29.462831" y="-5.54"> p</t年代p一个n> <tspan style="font-size: 12.50px; " x="59.02" y="-14.76"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="68.047165" y="-14.76"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="71.960602" y="-14.76"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,172.06,56.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,175.52,59.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,182.86,64.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n> </text> <g> <path d="m 153.93,53.68 34.01,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,167.13,41.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="22" y="-1.42"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="33.459999" y="-8.75"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,205.46,47.43)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,216.31,50.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="52.349998" y="-8.0600004"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="9.7600002" y="-10.57"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="18.787167" y="-10.57"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="30.127386" y="-10.57"> e</t年代p一个n> <tspan style="font-size: 12.50px; " x="35.678719" y="-10.57"> x</t年代p一个n> <tspan style="font-size: 12.50px; " x="41.930218" y="-10.57"> p</t年代p一个n> <tspan style="font-size: 12.50px; " x="58.200001" y="-10.57"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="66.764557" y="-10.57"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="75.791718" y="-10.57"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="79.705162" y="-10.57"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,301.21,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,304.66,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,312,66.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,317.08,61.13)"> <tspan style="font-size: 12.50px; " x="11.09" y="2.51"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代p一个n> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> </t年代p一个n> </text> <g> <path d="m 226.07,53.68 107.95,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,273.84,41.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,281.18,45.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,335.22,50.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="-184.32001" y="22.469999"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,157.15,24.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ×</t年代p一个n> <tspan style="font-size: 8.75px; " x="9.9772797" y="0"> 3</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,275.41,28.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,280.27,24.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,344.24,57.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⎞</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="10.75"> ⎟</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="21.51"> ⎟</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="32.200001"> ⎠</t年代p一个n> <tspan style="font-size: 12.50px; " x="7.71" y="12.94"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="-272.07999" y="73.769997"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,77.72,-10.81)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="5.837584" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,88.22,-12.99)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,90.83,-10.81)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Δ</t年代p一个n> <tspan style="font-size: 8.75px; " x="6.318944" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,103.86,-15.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.04" y="-18.32"> ⎛</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.04" y="-7.5700002"> ⎜</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.04" y="3.1900001"> ⎜</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.04" y="13.94"> ⎜</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.04" y="24.629999"> ⎝</t年代p一个n> <tspan style="font-size: 12.50px; " x="69.889999" y="-22.43"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,178.62,3.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,278.22,6.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,284.47,3.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ×</t年代p一个n> <tspan style="font-size: 8.75px; " x="9.9772797" y="0"> 3</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,122.72,-17.91)"> <tspan style="font-size: 12.50px; " x="42.59" y="2.51"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="20.367388" y="0"> e</t年代p一个n> <tspan style="font-size: 12.50px; " x="25.918718" y="0"> x</t年代p一个n> <tspan style="font-size: 12.50px; " x="32.170219" y="0"> p</t年代p一个n> <tspan style="font-size: 12.50px; " x="48.439999" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="57.004555" y="0"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="66.031723" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="69.94516" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,199.32,-21.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,202.78,-17.91)"> <tspan style="font-size: 12.50px; " x="16.870001" y="2.51"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="7.3267579" y="0"> /</t年代p一个n> <tspan style="font-size: 12.50px; " x="10.802592" y="0"> </t年代p一个n> </text> <g> <path d="m 122.72,-25.36 102.78,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,170.44,-37.24)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="93.480003" y="-1.4299999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="102.86" y="-8.7600002"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="56.25" y="-8.7600002"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="71.253601" y="-8.7600002"> e</t年代p一个n> <tspan style="font-size: 12.50px; " x="76.804932" y="-8.7600002"> x</t年代p一个n> <tspan style="font-size: 12.50px; " x="83.056435" y="-8.7600002"> p</t年代p一个n> <tspan style="font-size: 12.50px; " x="112.62" y="-17.98"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="121.64716" y="-17.98"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="125.56061" y="-17.98"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,302.65,-22.38)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,306.11,-19.26)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <g> <path d="m 283.06,-25.36 30.38,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,295.22,-37.24)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="19.42" y="-1.4299999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="30.879999" y="-8.7600002"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,330.96,-31.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,335.84,2.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⎞</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="10.75"> ⎟</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="21.51"> ⎟</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="32.259998"> ⎟</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="42.950001"> ⎠</t年代p一个n> <tspan style="font-size: 12.50px; " x="7.71" y="18.32"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="138.28" y="-9.9700003"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="142.4435" y="-9.9700003"> 6</t年代p一个n> <tspan style="font-size: 12.50px; " x="148.69499" y="-9.9700003"> )</t年代p一个n> </text> </g> </g> </svg></span>在这里,时间可逆系数和条件<年代vg height="20.174999" id="M41" style="vertical-align:-3.79959pt;width:138.0625px;" version="1.1" viewbox="0 0 138.0625 20.174999" width="138.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,20.175)"> <g transform="translate(72,-55.86)"> <text transform="matrix(1,0,0,-1,-71.95,59.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∑</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-60.52,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5</t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="9.9399996"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="2.7831359" y="9.9399996"> =</t年代p一个n> <tspan style="font-size: 8.75px; " x="8.7782564" y="9.9399996"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-44.79,59.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-39.6,56.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-32.67,59.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.04" y="0.029999999"> ∑</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-9.2,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5</t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="9.9399996"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="2.7831359" y="9.9399996"> =</t年代p一个n> <tspan style="font-size: 8.75px; " x="8.7782564" y="9.9399996"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,6.53,59.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,13.19,56.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,20.12,59.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代p一个n> </text> </g> </g> </svg>已经被考虑。与这些假设,我们只有三个系数,即<年代vg height="14.6625" id="M42" style="vertical-align:-3.13504pt;width:67.712502px;" version="1.1" viewbox="0 0 67.712502 14.6625" width="67.712502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6625)"> <g transform="translate(72,-60.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> {</t年代p一个n> <tspan style="font-size: 12.50px; " x="6.00144" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-60.76,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-55.89,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-45.49,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-40.61,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-28.75,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-23.88,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</t年代p一个n> </text> </g> </g> </svg>有待确定。使用Baker-Campbell-Hausdorff (BCH)公式的显式表达式<年代vg height="14.5625" id="M43" style="vertical-align:-3.13504pt;width:17.5px;" version="1.1" viewbox="0 0 17.5 14.5625" width="17.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5625)"> <g transform="translate(72,-60.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Υ</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-62.92,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> </g> </g> </svg>和<年代vg height="14.5625" id="M44" style="vertical-align:-3.13504pt;width:17.5px;" version="1.1" viewbox="0 0 17.5 14.5625" width="17.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5625)"> <g transform="translate(72,-60.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Υ</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-62.92,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> </g> </g> </svg>可以表示为<年代p一个nclass="equation" id="EEq9"> <svg height="92.525002" id="M45" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 92.525002" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,92.525)"> <g transform="translate(72,2.02)"> <text transform="matrix(1,0,0,-1,68.6,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Υ</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,77.63,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,85.97,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,104.95,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,111.91,63.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="18.4" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1599998" y="-0.039999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="13.187166" y="-0.039999999"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="22.559999" y="-0.039999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="31.587166" y="-0.039999999"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="36.788414" y="-0.039999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="45.139999" y="0"> ]</t年代p一个n> <tspan style="font-size: 12.50px; " x="49.303497" y="0"> ]</t年代p一个n> <tspan style="font-size: 12.50px; " x="56.25" y="-0.039999999"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="67.577721" y="-0.039999999"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,186.44,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,193.4,63.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="18.4" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="55.549999" y="-0.039999999"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="-124.8" y="20.440001"> Υ</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1599998" y="-0.039999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="13.187166" y="-0.039999999"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="22.559999" y="-0.039999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="31.587166" y="-0.039999999"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="36.788414" y="-0.039999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="45.139999" y="0"> ]</t年代p一个n> <tspan style="font-size: 12.50px; " x="49.303497" y="0"> ]</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,77.63,39.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,85.97,42.72)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,104.95,39.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,111.91,42.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="18.4" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="36.799999" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="55.200001" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1599998" y="-0.029999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="13.187166" y="-0.029999999"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="22.559999" y="-0.029999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="31.587166" y="-0.029999999"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="40.959999" y="-0.029999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="49.987167" y="-0.029999999"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="59.360001" y="-0.029999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="68.387169" y="-0.029999999"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="73.600914" y="-0.029999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="81.940002" y="0"> ]</t年代p一个n> <tspan style="font-size: 12.50px; " x="86.1035" y="0"> ]</t年代p一个n> <tspan style="font-size: 12.50px; " x="90.266998" y="0"> ]</t年代p一个n> <tspan style="font-size: 12.50px; " x="94.430496" y="0"> ]</t年代p一个n> <tspan style="font-size: 12.50px; " x="101.37" y="-0.029999999"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="112.71022" y="-0.029999999"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,231.57,39.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,238.52,42.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="18.4" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="36.799999" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="54.52" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1700001" y="-0.029999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="13.197166" y="-0.029999999"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="22.57" y="-0.029999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="31.597166" y="-0.029999999"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="40.970001" y="-0.029999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="49.309502" y="-0.029999999"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="58.68" y="-0.029999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="67.707169" y="-0.029999999"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="72.908417" y="-0.029999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="81.260002" y="0"> ]</t年代p一个n> <tspan style="font-size: 12.50px; " x="85.4235" y="0"> ]</t年代p一个n> <tspan style="font-size: 12.50px; " x="89.586998" y="0"> ]</t年代p一个n> <tspan style="font-size: 12.50px; " x="93.750496" y="0"> ]</t年代p一个n> <tspan style="font-size: 12.50px; " x="-143.28" y="20.440001"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="-131.93977" y="20.440001"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,113.52,19.13)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,120.48,22.21)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="17.719999" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="36.119999" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="54.52" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1700001" y="-0.039999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="12.509501" y="-0.039999999"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="21.879999" y="-0.039999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="30.907166" y="-0.039999999"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="40.279999" y="-0.039999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="49.307167" y="-0.039999999"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="58.68" y="-0.039999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="67.707169" y="-0.039999999"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="72.908417" y="-0.039999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="81.260002" y="0"> ]</t年代p一个n> <tspan style="font-size: 12.50px; " x="85.4235" y="0"> ]</t年代p一个n> <tspan style="font-size: 12.50px; " x="89.586998" y="0"> ]</t年代p一个n> <tspan style="font-size: 12.50px; " x="93.750496" y="0"> ]</t年代p一个n> <tspan style="font-size: 12.50px; " x="100.69" y="-0.039999999"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="112.03022" y="-0.039999999"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,239.45,19.13)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 6</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,246.41,22.21)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="17.709999" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="35.419998" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="53.139999" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1599998" y="-0.039999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="12.499501" y="-0.039999999"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="21.879999" y="-0.039999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="30.219501" y="-0.039999999"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="39.59" y="-0.039999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="47.929501" y="-0.039999999"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="57.299999" y="-0.039999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="66.327164" y="-0.039999999"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="71.528412" y="-0.039999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="79.879997" y="0"> ]</t年代p一个n> <tspan style="font-size: 12.50px; " x="84.043503" y="0"> ]</t年代p一个n> <tspan style="font-size: 12.50px; " x="88.207001" y="0"> ]</t年代p一个n> <tspan style="font-size: 12.50px; " x="92.370499" y="0"> ]</t年代p一个n> <tspan style="font-size: 12.50px; " x="-151.17" y="20.43"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="-139.82977" y="20.43"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,113.52,-1.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 7</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,120.48,1.74)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="17.719999" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="35.43" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="53.830002" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1700001" y="-0.039999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="12.509501" y="-0.039999999"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="21.879999" y="-0.039999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="30.219501" y="-0.039999999"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="39.59" y="-0.039999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="48.617165" y="-0.039999999"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="57.990002" y="-0.039999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="67.017166" y="-0.039999999"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="72.218414" y="-0.039999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="80.57" y="0"> ]</t年代p一个n> <tspan style="font-size: 12.50px; " x="84.733498" y="0"> ]</t年代p一个n> <tspan style="font-size: 12.50px; " x="88.896996" y="0"> ]</t年代p一个n> <tspan style="font-size: 12.50px; " x="93.060493" y="0"> ]</t年代p一个n> <tspan style="font-size: 12.50px; " x="100" y="-0.039999999"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="111.34022" y="-0.039999999"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,238.76,-1.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 8</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,245.72,1.74)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="18.4" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="36.110001" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="53.830002" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="99.309998" y="-0.039999999"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1700001" y="-0.039999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="13.197166" y="-0.039999999"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="22.57" y="-0.039999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="30.9095" y="-0.039999999"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="40.279999" y="-0.039999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="48.619499" y="-0.039999999"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="57.990002" y="-0.039999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="67.017166" y="-0.039999999"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="72.218414" y="-0.039999999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="80.57" y="0"> ]</t年代p一个n> <tspan style="font-size: 12.50px; " x="84.733498" y="0"> ]</t年代p一个n> <tspan style="font-size: 12.50px; " x="88.896996" y="0"> ]</t年代p一个n> <tspan style="font-size: 12.50px; " x="93.060493" y="0"> ]</t年代p一个n> <tspan style="font-size: 12.50px; " x="228.39999" y="-30.120001"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="232.56349" y="-30.120001"> 7</t年代p一个n> <tspan style="font-size: 12.50px; " x="238.815" y="-30.120001"> )</t年代p一个n> </text> </g> </g> </svg></span>在这里,<年代vg height="13.35" id="M46" style="vertical-align:-1.95624pt;width:119.2125px;" version="1.1" viewbox="0 0 119.2125 13.35" width="119.2125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.35)"> <g transform="translate(72,-61.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="18.391912" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="26.731415" y="0"> ]</t年代p一个n> <tspan style="font-size: 12.50px; " x="34.370747" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="46.411137" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="55.438301" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="66.553467" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="77.893692" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="86.233192" y="0"> </t年代p一个n> </text> </g> </g> </svg>和<年代vg height="14.775" id="M47" style="vertical-align:-3.2316pt;width:220.10001px;" version="1.1" viewbox="0 0 220.10001 14.775" width="220.10001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.775)"> <g transform="translate(72,-60.18)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-65.01,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-58.32,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-39.34,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-36.12,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-26.77,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-21.89,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-11.5,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-6.62,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,5.24,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,10.11,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="13.540749" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="20.905016" y="0"> ∈</t年代p一个n> <tspan style="font-size: 12.50px; " x="32.932903" y="0"> {</t年代p一个n> <tspan style="font-size: 12.50px; " x="38.934341" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="45.185841" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="50.399593" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="56.651093" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="61.864845" y="0"> …</t年代p一个n> <tspan style="font-size: 12.50px; " x="76.443344" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="81.657089" y="0"> 8</t年代p一个n> <tspan style="font-size: 12.50px; " x="87.908592" y="0"> }</t年代p一个n> </text> </g> </g> </svg>。详细的表达<年代vg height="14.5875" id="M48" style="vertical-align:-3.2316pt;width:12.825px;" version="1.1" viewbox="0 0 12.825 14.5875" width="12.825" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5875)"> <g transform="translate(72,-60.33)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-65.01,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>可以成立于<一个href="#B14">13</一个>]。公式(<一个href="#EEq6">5</一个>)代表一个四阶方案<年代vg height="14.6" id="M49" style="vertical-align:-3.13504pt;width:44.700001px;" version="1.1" viewbox="0 0 44.700001 14.6" width="44.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Υ</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-62.92,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-54.58,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 0</t年代p一个n> </text> </g> </g> </svg>,也就是说,<年代vg height="14.475" id="M50" style="vertical-align:-3.13504pt;width:14.8875px;" version="1.1" viewbox="0 0 14.8875 14.475" width="14.8875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-65.01,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> </g> </g> </svg>和<年代vg height="14.475" id="M51" style="vertical-align:-3.13504pt;width:14.8875px;" version="1.1" viewbox="0 0 14.8875 14.475" width="14.8875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-65.01,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> </g> </g> </svg>等于零。现在,我们有三个系数,只有两个方程,我们可以设置一个方程。在本文中,我们选择减少基于截断误差<年代vg height="14.5625" id="M52" style="vertical-align:-3.13504pt;width:17.5px;" version="1.1" viewbox="0 0 17.5 14.5625" width="17.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5625)"> <g transform="translate(72,-60.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Υ</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-62.92,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> </g> </g> </svg>至少,系数<年代vg height="14.6625" id="M53" style="vertical-align:-3.13504pt;width:67.712502px;" version="1.1" viewbox="0 0 67.712502 14.6625" width="67.712502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6625)"> <g transform="translate(72,-60.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> {</t年代p一个n> <tspan style="font-size: 12.50px; " x="6.00144" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-60.76,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-55.89,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-45.49,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-40.61,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-28.75,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-23.88,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</t年代p一个n> </text> </g> </g> </svg>可以通过求解方程组获得<年代p一个nclass="equation" id="EEq11"> <svg height="123.55" id="M54" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 123.55" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,123.55)"> <g transform="translate(72,26.84)"> <text transform="matrix(1,0,0,-1,118.57,43.64)"> <tspan style="font-size: 12.50px; " x="63.48" y="-13.25"> ⎧</t年代p一个n> <tspan style="font-size: 12.50px; " x="63.48" y="-7.1900001"> ⎪</t年代p一个n> <tspan style="font-size: 12.50px; " x="63.48" y="3.1900001"> ⎨</t年代p一个n> <tspan style="font-size: 12.50px; " x="63.48" y="13.57"> ⎪</t年代p一个n> <tspan style="font-size: 12.50px; " x="63.48" y="19.57"> ⎩</t年代p一个n> <tspan style="font-size: 12.50px; " x="71.480003" y="-19.66"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="71.480003" y="-12.75"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="71.480003" y="-5.8400002"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="71.480003" y="16.33"> ⎷</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="0"> 米</t年代p一个n> <tspan style="font-size: 12.50px; " x="9.727334" y="0"> 我</t年代p一个n> <tspan style="font-size: 12.50px; " x="13.203168" y="0"> n</t年代p一个n> </text> <g> <path d="m 204.85,70.71 87.41,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,210.74,59.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 8</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,204.85,37.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,206.38,29.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> =</t年代p一个n> <tspan style="font-size: 8.75px; " x="8.7169924" y="0"> 3</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,223.09,43.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,231.53,48.71)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 8.75px; " x="-1.5" y="8.6899996"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,238.49,41.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,249.53,40.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,254.4,43.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,264.8,40.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,269.67,43.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,281.54,40.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,286.41,41.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="5.8499999" y="-15.76"> ⎫</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.8499999" y="-9.6999998"> ⎪</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.8499999" y="0.68000001"> ⎬</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.8499999" y="11.06"> ⎪</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.8499999" y="17.120001"> ⎭</t年代p一个n> <tspan style="font-size: 12.50px; " x="-97.43" y="36.84"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="-169.92" y="50.099998"> 年代</t年代p一个n> <tspan style="font-size: 12.50px; " x="-165.05634" y="50.099998"> u</t年代p一个n> <tspan style="font-size: 12.50px; " x="-158.80484" y="50.099998"> b</t年代p一个n> <tspan style="font-size: 12.50px; " x="-152.55333" y="50.099998"> j</t年代p一个n> <tspan style="font-size: 12.50px; " x="-149.0775" y="50.099998"> e</t年代p一个n> <tspan style="font-size: 12.50px; " x="-143.52617" y="50.099998"> c</t年代p一个n> <tspan style="font-size: 12.50px; " x="-137.97484" y="50.099998"> t</t年代p一个n> <tspan style="font-size: 12.50px; " x="-131.38576" y="50.099998"> t</t年代p一个n> <tspan style="font-size: 12.50px; " x="-127.92242" y="50.099998"> o</t年代p一个n> <tspan style="font-size: 12.50px; " x="-121.67092" y="50.099998"> :</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,195.92,1.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,202.88,1.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,213.92,1.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,218.79,4.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,229.19,1.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,234.06,4.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,245.93,1.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,250.8,1.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="-63.380001" y="24.01"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="9.3199997" y="-2.51"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="21.36039" y="-2.51"> 0</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,194.36,-25.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,201.31,-24.74)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="5.8600001" y="-2.51"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,212.35,-25.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,217.23,-22.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,227.63,-25.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,232.5,-22.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,244.36,-25.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,249.24,-24.74)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="9.3199997" y="-2.51"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="21.347885" y="-2.51"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="27.599386" y="-2.51"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="224.88" y="-44.189999"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="229.0435" y="-44.189999"> 8</t年代p一个n> <tspan style="font-size: 12.50px; " x="235.295" y="-44.189999"> )</t年代p一个n> </text> </g> </g> </svg></span>一个可能的组系数c<年代ub>1</年代ub>c = 0.1786,<年代ub>2</年代ub>=−0.0066 d<年代ub>1</年代ub>0.00093 = 0.7123,由全球最小截断误差。现在,我们转移到空间域离散化。</p> <h5 id="sec2.3">2.3。Mth-Order差分逼近的一阶空间偏微分算子</h5> <p>让<年代vg height="18.512501" id="M55" style="vertical-align:-5.7006pt;width:191.39999px;" version="1.1" viewbox="0 0 191.39999 18.512501" width="191.39999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.5125)"> <g transform="translate(72,-57.19)"> <text transform="matrix(1,0,0,-1,-71.95,62.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> |</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-62.51,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="2.7218721" y="9.2200003"> ,</t年代p一个n> <tspan style="font-size: 8.75px; " x="4.9098721" y="9.2200003"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="8.3143997" y="9.2200003"> ,</t年代p一个n> <tspan style="font-size: 8.75px; " x="10.5024" y="9.2200003"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-43.29,62.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="18.967051" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="23.13055" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="27.018984" y="0"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="36.04615" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="42.922798" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="48.136551" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="53.000217" y="0"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="62.027382" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="68.228874" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="73.430122" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="80.206741" y="0"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="89.23391" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="95.472908" y="0"> ;</t年代p一个n> <tspan style="font-size: 12.50px; " x="101.03674" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="107.25073" y="0"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="116.2779" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="120.19134" y="0"> )</t年代p一个n> </text> </g> </g> </svg>接近精确解<年代vg height="13.4875" id="M56" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>在点<年代vg height="13.6125" id="M57" style="vertical-align:-2.34499pt;width:100.9625px;" version="1.1" viewbox="0 0 100.9625 13.6125" width="100.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="8.0519323" y="0"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="17.079098" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="23.955748" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="29.156996" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="34.020664" y="0"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="43.047829" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="49.249317" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="54.463066" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="61.239693" y="0"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="70.266861" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="76.505859" y="0"> )</t年代p一个n> </text> </g> </g> </svg>在<我>n</我>时间步长。下面的交错<年代vg height="10.325" id="M58" style="vertical-align:-0.0pt;width:17.237499px;" version="1.1" viewbox="0 0 17.237499 10.325" width="17.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>阶空间不同运营商使用近似的一阶空间偏导数<年代vg height="13.425" id="M59" style="vertical-align:-2.29482pt;width:8.4875002px;" version="1.1" viewbox="0 0 8.4875002 13.425" width="8.4875002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>方向,<年代vg height="16.6625" id="M60" style="vertical-align:-4.74141pt;width:101.025px;" version="1.1" viewbox="0 0 101.025 16.6625" width="101.025" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6625)"> <g transform="translate(72,-58.67)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-65.56,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-60.38,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="15.366187" y="0"> ∈</t年代p一个n> <tspan style="font-size: 12.50px; " x="27.406576" y="0"> {</t年代p一个n> <tspan style="font-size: 12.50px; " x="33.408016" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="40.284664" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="45.485912" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="51.687401" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="56.901154" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="63.140148" y="0"> }</t年代p一个n> </text> </g> </g> </svg>在三维卷曲运营商<年代vg height="10.6875" id="M61" style="vertical-align:-0.0pt;width:11.4125px;" version="1.1" viewbox="0 0 11.4125 10.6875" width="11.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6875)"> <g transform="translate(72,-63.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>。所以<年代p一个nclass="equation" id="EEq12"> <svg height="125.8625" id="M62" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 125.8625" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,125.8625)"> <g transform="translate(72,28.69)"> <text transform="matrix(1,0,0,-1,76.27,55.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℜ</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,87.19,52.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,93.19,55.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</t年代p一个n> <tspan style="font-size: 12.50px; " x="6.3515239" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,107.99,60.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="-1.5" y="9.2200003"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="1.221872" y="9.2200003"> ,</t年代p一个n> <tspan style="font-size: 8.75px; " x="3.4098721" y="9.2200003"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="6.8144002" y="9.2200003"> ,</t年代p一个n> <tspan style="font-size: 8.75px; " x="9.0024004" y="9.2200003"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,123.43,55.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≡</t年代p一个n> <tspan style="font-size: 12.50px; " x="16.67" y="-7.25"> </t年代p一个n> </text> <g> <path d="m 136.66,58.89 13.27,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,136.66,47.02)"> <tspan style="font-size: 12.50px; " x="14.46" y="-8.75"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="22.9" y="-15.67"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="22.9" y="-5"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="22.9" y="-1.84"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="6.3765302" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,162.06,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="21.879999"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="2.7218721" y="21.879999"> ,</t年代p一个n> <tspan style="font-size: 8.75px; " x="4.9098721" y="21.879999"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="8.3143997" y="21.879999"> ,</t年代p一个n> <tspan style="font-size: 8.75px; " x="10.5024" y="21.879999"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,125.7,11.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="18.059999" y="-7.2600002"> 1</t年代p一个n> </text> <g> <path d="m 138.94,14.4 15.9,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,138.94,2.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,156.31,27.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="8.7957602" y="0"> /</t年代p一个n> <tspan style="font-size: 8.75px; " x="11.228816" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,156.04,4.72)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,157,-2.46)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> =</t年代p一个n> <tspan style="font-size: 8.75px; " x="9.8459997" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,172.19,11.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,178.23,8.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,184.66,6.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="6.9400001" y="-4.9200001"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="15.38" y="-6.5100002"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="15.38" y="-3.3499999"> |</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,202.54,18.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="10.98"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="2.7218721" y="10.98"> +</t年代p一个n> <tspan style="font-size: 8.75px; " x="8.7169924" y="10.98"> (</t年代p一个n> <tspan style="font-size: 8.75px; " x="11.631408" y="10.98"> 2</t年代p一个n> <tspan style="font-size: 8.75px; " x="16.007408" y="10.98"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="19.858288" y="10.98"> −</t年代p一个n> <tspan style="font-size: 8.75px; " x="25.853409" y="10.98"> 1</t年代p一个n> <tspan style="font-size: 8.75px; " x="30.229408" y="10.98"> )</t年代p一个n> <tspan style="font-size: 8.75px; " x="33.143826" y="10.98"> /</t年代p一个n> <tspan style="font-size: 8.75px; " x="35.576881" y="10.98"> 2</t年代p一个n> <tspan style="font-size: 8.75px; " x="39.952881" y="10.98"> ,</t年代p一个n> <tspan style="font-size: 8.75px; " x="42.140881" y="10.98"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="45.545406" y="10.98"> ,</t年代p一个n> <tspan style="font-size: 8.75px; " x="47.73341" y="10.98"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,258.29,11.27)"> <tspan style="font-size: 12.50px; " x="20.98" y="-1.59"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="20.98" y="1.5700001"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.528006" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,281.77,18.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="10.98"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="2.7218721" y="10.98"> −</t年代p一个n> <tspan style="font-size: 8.75px; " x="8.7169924" y="10.98"> (</t年代p一个n> <tspan style="font-size: 8.75px; " x="11.631408" y="10.98"> 2</t年代p一个n> <tspan style="font-size: 8.75px; " x="16.007408" y="10.98"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="19.858288" y="10.98"> −</t年代p一个n> <tspan style="font-size: 8.75px; " x="25.853409" y="10.98"> 1</t年代p一个n> <tspan style="font-size: 8.75px; " x="30.229408" y="10.98"> )</t年代p一个n> <tspan style="font-size: 8.75px; " x="33.143826" y="10.98"> /</t年代p一个n> <tspan style="font-size: 8.75px; " x="35.576881" y="10.98"> 2</t年代p一个n> <tspan style="font-size: 8.75px; " x="39.952881" y="10.98"> ,</t年代p一个n> <tspan style="font-size: 8.75px; " x="42.140881" y="10.98"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="45.545406" y="10.98"> ,</t年代p一个n> <tspan style="font-size: 8.75px; " x="47.73341" y="10.98"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,334.75,6.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="-199.78" y="31.24"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="-188.43977" y="31.24"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="-179.03752" y="31.24"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="-174.87402" y="31.24"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="-165.84686" y="31.24"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="-158.97021" y="31.24"> )</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,179.95,-19.71)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,190.03,-24.89)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="284.09" y="-43.419998"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="288.25351" y="-43.419998"> 9</t年代p一个n> <tspan style="font-size: 12.50px; " x="294.505" y="-43.419998"> )</t年代p一个n> </text> </g> </g> </svg></span>在这里,参数<年代vg height="18.012501" id="M63" style="vertical-align:-3.2316pt;width:167.875px;" version="1.1" viewbox="0 0 167.875 18.012501" width="167.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.0125)"> <g transform="translate(72,-57.59)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-65.91,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-58.09,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="24.755939" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="31.007441" y="0"> )</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-22.91,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> +</t年代p一个n> <tspan style="font-size: 8.75px; " x="9.8459997" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-8.19,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="8.3269978" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="23.668179" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="35.0084" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="41.259899" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="45.423401" y="0"> !</t年代p一个n> <tspan style="font-size: 12.50px; " x="51.6749" y="0"> !</t年代p一个n> <tspan style="font-size: 12.50px; " x="57.913895" y="0"> )</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,53.9,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,58.77,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代p一个n> </text> </g> </g> </svg> <svg height="16.75" id="M64" style="vertical-align:-2.21957pt;width:255.875px;" version="1.1" viewbox="0 0 255.875 16.75" width="255.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.75)"> <g transform="translate(72,-58.6)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-65.7,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="8.7957602" y="0"> −</t年代p一个n> <tspan style="font-size: 8.75px; " x="14.79088" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-46.03,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="16.729013" y="0"> /</t年代p一个n> <tspan style="font-size: 12.50px; " x="20.204847" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="29.219511" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="40.572235" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="48.84922" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="60.189442" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="66.440941" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="70.604439" y="0"> !</t年代p一个n> <tspan style="font-size: 12.50px; " x="76.855942" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="81.01944" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="93.584953" y="0"> /</t年代p一个n> <tspan style="font-size: 12.50px; " x="97.060791" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="106.08795" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="117.42818" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="122.9295" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="127.09299" y="0"> !</t年代p一个n> <tspan style="font-size: 12.50px; " x="133.3445" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="137.508" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="143.75949" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="152.03648" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="163.37669" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="169.6282" y="0"> )</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,127.77,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> </g> </g> </svg>(最小截断误差的<一个href="#EEq12">9</一个>)。同样的,<年代vg height="18.512501" id="M65" style="vertical-align:-5.80093pt;width:59.087502px;" version="1.1" viewbox="0 0 59.087502 18.512501" width="59.087502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.5125)"> <g transform="translate(72,-57.19)"> <text transform="matrix(1,0,0,-1,-71.95,63.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℜ</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-61.02,59.89)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-53.82,63.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</t年代p一个n> <tspan style="font-size: 12.50px; " x="6.3515239" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-39.02,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="-1.5" y="9.2200003"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="1.221872" y="9.2200003"> ,</t年代p一个n> <tspan style="font-size: 8.75px; " x="3.4098721" y="9.2200003"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="6.8144002" y="9.2200003"> ,</t年代p一个n> <tspan style="font-size: 8.75px; " x="9.0024004" y="9.2200003"> </t年代p一个n> </text> </g> </g> </svg>和<年代vg height="18.512501" id="M66" style="vertical-align:-5.80093pt;width:60.112499px;" version="1.1" viewbox="0 0 60.112499 18.512501" width="60.112499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.5125)"> <g transform="translate(72,-57.19)"> <text transform="matrix(1,0,0,-1,-71.95,63.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℜ</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-61.02,59.89)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-53,63.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</t年代p一个n> <tspan style="font-size: 12.50px; " x="6.3515239" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-38.21,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="-1.5" y="9.2200003"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="1.221872" y="9.2200003"> ,</t年代p一个n> <tspan style="font-size: 8.75px; " x="3.4098721" y="9.2200003"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="6.8144002" y="9.2200003"> ,</t年代p一个n> <tspan style="font-size: 8.75px; " x="9.0024004" y="9.2200003"> </t年代p一个n> </text> </g> </g> </svg>构建以类似的方式,用来近似<年代vg height="18.512501" id="M67" style="vertical-align:-5.80093pt;width:42.512501px;" version="1.1" viewbox="0 0 42.512501 18.512501" width="42.512501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.5125)"> <g transform="translate(72,-57.19)"> <text transform="matrix(1,0,0,-1,-71.95,63.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-65.56,59.89)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-60.72,63.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-52.28,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="-1.5" y="9.2200003"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="1.221872" y="9.2200003"> ,</t年代p一个n> <tspan style="font-size: 8.75px; " x="3.4098721" y="9.2200003"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="6.8144002" y="9.2200003"> ,</t年代p一个n> <tspan style="font-size: 8.75px; " x="9.0024004" y="9.2200003"> </t年代p一个n> </text> </g> </g> </svg>和<年代vg height="18.512501" id="M68" style="vertical-align:-5.80093pt;width:42.549999px;" version="1.1" viewbox="0 0 42.549999 18.512501" width="42.549999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.5125)"> <g transform="translate(72,-57.19)"> <text transform="matrix(1,0,0,-1,-71.95,63.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-65.56,59.89)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-60.7,63.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-52.26,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="-1.5" y="9.2200003"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="1.221872" y="9.2200003"> ,</t年代p一个n> <tspan style="font-size: 8.75px; " x="3.4098721" y="9.2200003"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="6.8144002" y="9.2200003"> ,</t年代p一个n> <tspan style="font-size: 8.75px; " x="9.0024004" y="9.2200003"> </t年代p一个n> </text> </g> </g> </svg>,分别。</p> <h4 id="practical-implementation">3所示。实际的实现</h4> <h5 id="sec3.1">3.1。明确的离散化公式</h5> <p>当一个使用系数<年代vg height="11.0375" id="M69" style="vertical-align:-3.22282pt;width:10.925px;" version="1.1" viewbox="0 0 10.925 11.0375" width="10.925" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0375)"> <g transform="translate(72,-63.17)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-66.76,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>和<年代vg height="14.5875" id="M70" style="vertical-align:-3.22282pt;width:12.7625px;" version="1.1" viewbox="0 0 12.7625 14.5875" width="12.7625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5875)"> <g transform="translate(72,-60.33)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-65.3,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>订单4和运营商与替代品的空间差异<年代vg height="10.325" id="M71" style="vertical-align:-0.0pt;width:17.237499px;" version="1.1" viewbox="0 0 17.237499 10.325" width="17.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>为一阶阶精度偏差运营商<年代vg height="10.6875" id="M72" style="vertical-align:-0.0pt;width:11.4125px;" version="1.1" viewbox="0 0 11.4125 10.6875" width="11.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6875)"> <g transform="translate(72,-63.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>,<年代vg height="13.45" id="M73" style="vertical-align:-2.21957pt;width:45.775002px;" version="1.1" viewbox="0 0 45.775002 13.45" width="45.775002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 4</t年代p一个n> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="19.779745" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="32.345261" y="0"> )</t年代p一个n> </text> </g> </g> </svg>方案。</p> <p>例如,使用绮网格(<一个href="#B1">1</一个>),的具体表达式<年代vg height="14.3375" id="M74" style="vertical-align:-3.21404pt;width:20.4125px;" version="1.1" viewbox="0 0 20.4125 14.3375" width="20.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-61.03,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>和<年代vg height="14.3375" id="M75" style="vertical-align:-3.21404pt;width:17.924999px;" version="1.1" viewbox="0 0 17.924999 14.3375" width="17.924999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-63.02,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>组件的<年代vg height="13.45" id="M76" style="vertical-align:-2.21957pt;width:45.775002px;" version="1.1" viewbox="0 0 45.775002 13.45" width="45.775002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 4</t年代p一个n> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="19.779745" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="32.345261" y="0"> )</t年代p一个n> </text> </g> </g> </svg>计划在<年代vg height="10.725" id="M77" style="vertical-align:-0.1254pt;width:5.4124999px;" version="1.1" viewbox="0 0 5.4124999 10.725" width="5.4124999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.725)"> <g transform="translate(72,-63.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>后阶段计算<年代vg height="7.1374998" id="M78" style="vertical-align:-0.10033pt;width:7.8874998px;" version="1.1" viewbox="0 0 7.8874998 7.1374998" width="7.8874998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>th时间步骤如下:<年代p一个nclass="equation" id="EEq13"> <svg height="345.17499" id="M79" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 345.17499" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,345.175)"> <g transform="translate(72,204.14)"> <text transform="matrix(1,0,0,-1,66.71,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,78.75,61.25)"> <tspan style="font-size: 8.75px; " x="-1.13" y="8.1300001"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> +</t年代p一个n> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="13.128" y="0"> /</t年代p一个n> <tspan style="font-size: 8.75px; " x="15.561056" y="0"> 5</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,101.27,51.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="36.639999" y="-12.17"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="7.3600001" y="-4.9200001"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="11.248433" y="-4.9200001"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="16.44968" y="-4.9200001"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="24.089014" y="-4.9200001"> +</t年代p一个n> </text> <g> <path d="m 137.91,59.37 6.25,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,137.91,47.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="34.75" y="-16.01"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="7.4499998" y="-8.7600002"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.651248" y="-8.7600002"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="22.203541" y="-8.7600002"> +</t年代p一个n> </text> <g> <path d="m 172.66,59.37 6.25,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,172.66,47.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="7.4499998" y="-3.8399999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="-68.220001" y="27.18"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="-102.48" y="24.67"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="-90.45211" y="24.67"> e</t年代p一个n> <tspan style="font-size: 12.50px; " x="-84.90078" y="24.67"> x</t年代p一个n> <tspan style="font-size: 12.50px; " x="-78.649284" y="24.67"> p</t年代p一个n> <tspan style="font-size: 12.50px; " x="-62.369999" y="24.67"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="-53.805447" y="24.67"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,128.55,19.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,133.42,20.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="8.6300001" y="-2.51"> ×</t年代p一个n> <tspan style="font-size: 12.50px; " x="19.407585" y="-2.51"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,164.87,28.87)"> <tspan style="font-size: 8.75px; " x="-1.12" y="8.71"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> +</t年代p一个n> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> (</t年代p一个n> <tspan style="font-size: 8.75px; " x="13.25928" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="16.042416" y="0"> −</t年代p一个n> <tspan style="font-size: 8.75px; " x="22.037537" y="0"> 1</t年代p一个n> <tspan style="font-size: 8.75px; " x="26.413536" y="0"> )</t年代p一个n> <tspan style="font-size: 8.75px; " x="29.327951" y="0"> /</t年代p一个n> <tspan style="font-size: 8.75px; " x="31.761007" y="0"> 5</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,203.59,17.9)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="36.639999" y="-12.18"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="7.3699999" y="-4.9200001"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="11.258433" y="-4.9200001"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="16.459681" y="-4.9200001"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="24.099014" y="-4.9200001"> +</t年代p一个n> </text> <g> <path d="m 240.23,25.95 6.26,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,240.23,14.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="34.75" y="-16.01"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="7.4499998" y="-8.75"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.651248" y="-8.75"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="22.203541" y="-8.75"> +</t年代p一个n> </text> <g> <path d="m 274.98,25.95 6.26,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,274.98,14.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="7.4499998" y="-3.8299999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="-195.53" y="30.360001"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="-140.39999" y="22.290001"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="-182.99001" y="19.780001"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="-173.97534" y="19.780001"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="-162.62262" y="19.780001"> e</t年代p一个n> <tspan style="font-size: 12.50px; " x="-157.07127" y="19.780001"> x</t年代p一个n> <tspan style="font-size: 12.50px; " x="-150.81978" y="19.780001"> p</t年代p一个n> <tspan style="font-size: 12.50px; " x="-134.55" y="19.780001"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="-125.98544" y="19.780001"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,158.69,-8.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,163.56,-8.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <g> <path d="m 91.99,-13.16 77.42,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,123.42,-25.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,133.11,-28.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,173.39,-16.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</t年代p一个n> <tspan style="font-size: 12.50px; " x="6.3499999" y="4.9200001"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="15.32" y="0"> ℜ</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,199.63,-19.41)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,207.65,-16.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</t年代p一个n> <tspan style="font-size: 12.50px; " x="6.3515239" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,223.69,-10.24)"> <tspan style="font-size: 8.75px; " x="-0.75" y="8.6999998"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> +</t年代p一个n> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> (</t年代p一个n> <tspan style="font-size: 8.75px; " x="13.25928" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="16.042416" y="0"> −</t年代p一个n> <tspan style="font-size: 8.75px; " x="22.037537" y="0"> 1</t年代p一个n> <tspan style="font-size: 8.75px; " x="26.413536" y="0"> )</t年代p一个n> <tspan style="font-size: 8.75px; " x="29.327951" y="0"> /</t年代p一个n> <tspan style="font-size: 8.75px; " x="31.761007" y="0"> 5</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,262.41,-21.21)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="36.639999" y="-12.17"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="7.3600001" y="-4.9200001"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="11.248433" y="-4.9200001"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="16.44968" y="-4.9200001"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="24.089014" y="-4.9200001"> +</t年代p一个n> </text> <g> <path d="m 299.05,-13.16 6.25,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,299.05,-25.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="34.75" y="-16"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="7.4499998" y="-8.75"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.651248" y="-8.75"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="22.203541" y="-8.75"> +</t年代p一个n> </text> <g> <path d="m 333.8,-13.16 6.25,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,333.8,-25.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="7.4499998" y="-3.8299999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="-174.14999" y="27.799999"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="-165.58545" y="27.799999"> ℜ</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,179.14,-55.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,186.35,-52.84)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</t年代p一个n> <tspan style="font-size: 12.50px; " x="6.3515239" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,202.38,-46.79)"> <tspan style="font-size: 8.75px; " x="-0.75" y="8.7799997"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> +</t年代p一个n> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> (</t年代p一个n> <tspan style="font-size: 8.75px; " x="13.25928" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="16.042416" y="0"> −</t年代p一个n> <tspan style="font-size: 8.75px; " x="22.037537" y="0"> 1</t年代p一个n> <tspan style="font-size: 8.75px; " x="26.413536" y="0"> )</t年代p一个n> <tspan style="font-size: 8.75px; " x="29.327951" y="0"> /</t年代p一个n> <tspan style="font-size: 8.75px; " x="31.761007" y="0"> 5</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,241.1,-57.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="36.639999" y="-12.18"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="7.3600001" y="-4.9200001"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="11.248433" y="-4.9200001"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="16.462185" y="-4.9200001"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="24.101517" y="-4.9200001"> +</t年代p一个n> </text> <g> <path d="m 277.74,-49.71 6.25,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,277.74,-61.59)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="34.75" y="-16.01"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="7.4499998" y="-8.75"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.651248" y="-8.75"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="22.203541" y="-8.75"> +</t年代p一个n> </text> <g> <path d="m 312.49,-49.71 6.26,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,312.49,-61.59)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="26.1" y="-8.75"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="-245.78" y="24.67"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="7.4499998" y="-3.8299999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="15.051824" y="-3.8299999"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,76.38,-81.26)"> <tspan style="font-size: 8.75px; " x="-0.75" y="8.1300001"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> +</t年代p一个n> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="13.128" y="0"> /</t年代p一个n> <tspan style="font-size: 8.75px; " x="15.561056" y="0"> 5</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,98.9,-91.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="26.57" y="-12.17"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="7.3699999" y="-4.9200001"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="14.034099" y="-4.9200001"> +</t年代p一个n> </text> <g> <path d="m 125.47,-83.13 6.26,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,125.47,-95.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="29.51" y="-3.8299999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="-21.030001" y="27.190001"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="7.4499998" y="-8.75"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.651248" y="-8.75"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="17.514915" y="-8.75"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="22.728666" y="-8.75"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="-55.290001" y="24.67"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="-43.262115" y="24.67"> e</t年代p一个n> <tspan style="font-size: 12.50px; " x="-37.710781" y="24.67"> x</t年代p一个n> <tspan style="font-size: 12.50px; " x="-31.459282" y="24.67"> p</t年代p一个n> <tspan style="font-size: 12.50px; " x="-15.18" y="24.67"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="-6.6154451" y="24.67"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,128.55,-122.81)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,133.42,-122.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="8.6300001" y="-2.52"> ×</t年代p一个n> <tspan style="font-size: 12.50px; " x="19.407585" y="-2.52"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,162.51,-113.63)"> <tspan style="font-size: 8.75px; " x="-0.75" y="8.71"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> +</t年代p一个n> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> (</t年代p一个n> <tspan style="font-size: 8.75px; " x="13.25928" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="16.042416" y="0"> −</t年代p一个n> <tspan style="font-size: 8.75px; " x="22.037537" y="0"> 1</t年代p一个n> <tspan style="font-size: 8.75px; " x="26.413536" y="0"> )</t年代p一个n> <tspan style="font-size: 8.75px; " x="29.327951" y="0"> /</t年代p一个n> <tspan style="font-size: 8.75px; " x="31.761007" y="0"> 5</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,201.23,-124.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="26.57" y="-12.17"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="7.3600001" y="-4.9200001"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="14.024099" y="-4.9200001"> +</t年代p一个n> </text> <g> <path d="m 227.8,-116.56 6.25,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,227.8,-128.43)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="29.5" y="-3.8299999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="-148.35001" y="30.360001"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="-93.220001" y="22.299999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="7.4400001" y="-8.75"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.653751" y="-8.75"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="17.517418" y="-8.75"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="22.718666" y="-8.75"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="-135.81" y="19.790001"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="-126.79533" y="19.790001"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="-115.44261" y="19.790001"> e</t年代p一个n> <tspan style="font-size: 12.50px; " x="-109.89128" y="19.790001"> x</t年代p一个n> <tspan style="font-size: 12.50px; " x="-103.63978" y="19.790001"> p</t年代p一个n> <tspan style="font-size: 12.50px; " x="-87.370003" y="19.790001"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="-78.805443" y="19.790001"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,158.69,-151.34)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,163.56,-150.73)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <g> <path d="m 91.99,-155.67 77.42,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,123.42,-167.55)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,133.11,-170.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,173.39,-158.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</t年代p一个n> <tspan style="font-size: 12.50px; " x="6.3499999" y="4.9200001"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="15.32" y="0"> ℜ</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,199.63,-161.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,206.84,-158.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</t年代p一个n> <tspan style="font-size: 12.50px; " x="6.3515239" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,225.24,-153.79)"> <tspan style="font-size: 8.75px; " x="-1.13" y="8.1300001"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> +</t年代p一个n> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="13.128" y="0"> /</t年代p一个n> <tspan style="font-size: 8.75px; " x="15.561056" y="0"> 5</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,247.76,-163.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="26.559999" y="-12.17"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="7.3600001" y="-4.9200001"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="14.024099" y="-4.9200001"> +</t年代p一个n> </text> <g> <path d="m 274.32,-155.67 6.26,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,274.32,-167.55)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="29.51" y="-3.8399999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="7.4499998" y="-8.7600002"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.651248" y="-8.7600002"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="17.514915" y="-8.7600002"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="22.728666" y="-8.7600002"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="-114.67" y="27.790001"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="-106.10545" y="27.790001"> ℜ</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,179.14,-198.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,187.16,-195.34)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</t年代p一个n> <tspan style="font-size: 12.50px; " x="6.3515239" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,205.56,-190.34)"> <tspan style="font-size: 8.75px; " x="-1.13" y="8.1300001"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> +</t年代p一个n> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="13.128" y="0"> /</t年代p一个n> <tspan style="font-size: 8.75px; " x="15.561056" y="0"> 5</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,228.08,-200.26)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="26.57" y="-12.17"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="7.3600001" y="-4.9200001"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="14.024099" y="-4.9200001"> +</t年代p一个n> </text> <g> <path d="m 254.65,-192.22 6.25,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,254.65,-204.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="7.4400001" y="-8.75"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.641248" y="-8.75"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="17.504915" y="-8.75"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="22.718666" y="-8.75"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="29.5" y="-3.8299999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="37.101826" y="-3.8299999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="213.22" y="-134.89"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="217.3835" y="-134.89"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="223.63499" y="-134.89"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="229.88651" y="-134.89"> )</t年代p一个n> </text> </g> </g> </svg></span>与<年代p一个nclass="equation" id="eq5"> <svg height="87.6875" id="M80" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 87.6875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,87.6875)"> <g transform="translate(72,-1.85)"> <text transform="matrix(1,0,0,-1,125.3,52.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,134.99,49.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,143.34,52.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="13.23" y="-9.2200003"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,161.76,58.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,165.21,61.63)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代p一个n> </text> <g> <path d="m 178.16,69.87 7.34,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,178.16,61.63)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,185.5,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,192.65,61.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="8.0519323" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="13.265683" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="20.905016" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="32.245235" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="38.496738" y="0"> /</t年代p一个n> <tspan style="font-size: 12.50px; " x="41.972572" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="48.224072" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="53.43782" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="62.990112" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="74.330338" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="80.581833" y="0"> /</t年代p一个n> <tspan style="font-size: 12.50px; " x="84.057671" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="90.309166" y="0"> )</t年代p一个n> </text> <g> <path d="m 156.57,55.53 130.56,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,169.76,43.65)"> <tspan style="font-size: 12.50px; " x="118.57" y="-8.7600002"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="-44.459999" y="30.01"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="9.6898251" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="13.853324" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="17.741756" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="22.955507" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="30.594841" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="41.947563" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="48.199066" y="0"> /</t年代p一个n> <tspan style="font-size: 12.50px; " x="51.6749" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="57.926399" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="63.127647" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="72.679939" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="84.032661" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="90.284164" y="0"> /</t年代p一个n> <tspan style="font-size: 12.50px; " x="93.759995" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="100.0115" y="0"> )</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,134.99,10.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,143.34,13.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="13.23" y="-9.2299995"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,163.22,19.75)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,166.68,22.87)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代p一个n> </text> <g> <path d="m 179.62,31.11 7.34,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,179.62,22.87)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="9.4147587" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="13.578258" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="20.242357" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="31.582579" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="37.83408" y="0"> /</t年代p一个n> <tspan style="font-size: 12.50px; " x="41.309914" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="47.573914" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="52.775162" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="57.638828" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="62.852581" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="69.629204" y="0"> )</t年代p一个n> </text> <g> <path d="m 156.57,16.77 96.85,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <g> <path d="m 168.74,12.64 6.05,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,168.74,4.24)"> <tspan style="font-size: 12.50px; " x="85.870003" y="-9.3999996"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="8.1269503" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.290449" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="18.954548" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="30.294769" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="36.546268" y="0"> /</t年代p一个n> <tspan style="font-size: 12.50px; " x="40.022102" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="46.273602" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="51.487354" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="56.351021" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="61.564774" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="68.3414" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="299.13" y="-29.559999"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="303.29349" y="-29.559999"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="309.54501" y="-29.559999"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="315.79651" y="-29.559999"> )</t年代p一个n> </text> </g> </g> </svg></span></p> <p>在这里<年代p一个nclass="list"><span class="list-item"><span class="list-label">(我)</年代p一个n><span class="list-content">我们使用Pade<年代vg height="13.45" id="M81" style="vertical-align:-2.21957pt;width:35.275002px;" version="1.1" viewbox="0 0 35.275002 13.45" width="35.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="17.704248" y="0"> 3</t年代p一个n> <tspan style="font-size: 12.50px; " x="23.955748" y="0"> )</t年代p一个n> </text> </g> </g> </svg>和Pade<年代vg height="13.45" id="M82" style="vertical-align:-2.21957pt;width:35.275002px;" version="1.1" viewbox="0 0 35.275002 13.45" width="35.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="17.704248" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="23.955748" y="0"> )</t年代p一个n> </text> </g> </g> </svg>近似的表达<年代vg height="14.7125" id="M83" style="vertical-align:-3.2316pt;width:65.150002px;" version="1.1" viewbox="0 0 65.150002 14.7125" width="65.150002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> e</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> x</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> p</t年代p一个n> <tspan style="font-size: 12.50px; " x="22.217831" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="26.38133" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="34.945885" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-27.31,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-24.09,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n> </text> </g> </g> </svg>和<年代vg height="14.7125" id="M84" style="vertical-align:-3.2316pt;width:121.5125px;" version="1.1" viewbox="0 0 121.5125 14.7125" width="121.5125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> e</t年代p一个n> <tspan style="font-size: 12.50px; " x="30.082218" y="0"> x</t年代p一个n> <tspan style="font-size: 12.50px; " x="36.333717" y="0"> p</t年代p一个n> <tspan style="font-size: 12.50px; " x="46.748718" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="50.912216" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="59.476772" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-2.77,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,0.45,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="8.3269978" y="0"> /</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,21.94,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>:</年代p一个n></span></span><span class="equation" id="EEq15"> <svg height="94.025002" id="M85" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 94.025002" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,94.025)"> <g transform="translate(72,3.22)"> <text transform="matrix(1,0,0,-1,116.15,56.25)"> <tspan style="font-size: 12.50px; " x="22.219999" y="2.52"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="0"> e</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> x</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> p</t年代p一个n> <tspan style="font-size: 12.50px; " x="28.07" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="36.634556" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,162.48,53.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,165.7,53.73)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="9.3199997" y="-2.52"> ≈</t年代p一个n> <tspan style="font-size: 12.50px; " x="74.480003" y="-9.7700005"> 1</t年代p一个n> </text> <g> <path d="m 188.26,59.37 110.1,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,188.26,45.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="9.0146627" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="20.367388" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,218.32,42.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,224.32,45.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,245.35,50.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="8.6899996"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,250.22,45.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代p一个n> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.503" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="23.843222" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,283.76,50.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="8.8199997"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,288.64,45.94)"> <tspan style="font-size: 12.50px; " x="10.92" y="-10.31"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="-120.88" y="26.58"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代p一个n> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> 6</t年代p一个n> <tspan style="font-size: 12.50px; " x="-163.47" y="24.07"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="-154.44284" y="24.07"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="-143.10262" y="24.07"> e</t年代p一个n> <tspan style="font-size: 12.50px; " x="-137.55128" y="24.07"> x</t年代p一个n> <tspan style="font-size: 12.50px; " x="-131.29977" y="24.07"> p</t年代p一个n> <tspan style="font-size: 12.50px; " x="-115.02" y="24.07"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="-106.45544" y="24.07"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,191.87,18.75)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,195.09,19.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <g> <path d="m 125.17,14.42 75.77,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,156.6,2.54)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,166.29,-0.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,205.61,11.3)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≈</t年代p一个n> <tspan style="font-size: 12.50px; " x="27.58" y="-9.2299995"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="36.594662" y="-9.2299995"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="47.947388" y="-9.2299995"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,263.25,17.41)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,266.47,20.53)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代p一个n> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> 2</t年代p一个n> </text> <g> <path d="m 218.84,14.42 71.7,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,218.84,1.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="20.367388" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,248.91,-2.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,254.91,1.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,275.94,5.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="8.6899996"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,280.81,1.12)"> <tspan style="font-size: 12.50px; " x="10.93" y="-10.18"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代p一个n> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> 3</t年代p一个n> <tspan style="font-size: 12.50px; " x="187.06" y="-30.139999"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="191.2235" y="-30.139999"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="197.47501" y="-30.139999"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="203.7265" y="-30.139999"> )</t年代p一个n> </text> </g> </g> </svg></span>我们的新近似获得超级稳定和效率比Pade[(2, 2)方法<一个href="#B15">14</一个>)当<年代vg height="11.3375" id="M86" style="vertical-align:-3.2316pt;width:16.262501px;" version="1.1" viewbox="0 0 16.262501 11.3375" width="16.262501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.3375)"> <g transform="translate(72,-62.93)"> <text transform="matrix(1,0,0,-1,-71.95,66.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-62.26,63.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>增加,显示在图<一个href="//www.newsama.com/journals/ijap/2012/956431/fig1/" target="_blank">1</一个>。此外,我们近似不仅可以用于治疗室内电介质和导体,而且直接应用于贝朗热的完美匹配层(PML)吸收边界条件<一个href="#B16">15</一个>]。<年代p一个nclass="list"><span class="list-item"><span class="list-label">(2)</年代p一个n><span class="list-content">的平均介电常数<年代vg height="12.35" id="M87" style="vertical-align:-0.13794pt;width:7.6875px;" version="1.1" viewbox="0 0 7.6875 12.35" width="7.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.35)"> <g transform="translate(72,-62.12)"> <g> <path d="m -71.95,70.71 6.05,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,62.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>在补丁<年代vg height="10.725" id="M88" style="vertical-align:-0.1254pt;width:11.375px;" version="1.1" viewbox="0 0 11.375 10.725" width="11.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.725)"> <g transform="translate(72,-63.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>可以表示为</年代p一个n></span></span><span class="equation" id="EEq17"> <svg height="38.862499" id="M89" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 38.862499" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,38.8625)"> <g transform="translate(72,-40.91)"> <g> <path d="m 120.78,63.04 6.05,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,120.78,54.64)"> <tspan style="font-size: 12.50px; " x="24.42" y="-7.25"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="9.5147829" y="0"> =</t年代p一个n> </text> <g> <path d="m 143.53,57.77 10.38,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,143.53,45.89)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,149.04,42.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,155.1,46.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,166.08,43.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,169.93,40.95)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,174.06,54.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,180.11,51.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,184.98,54.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="6.6515961" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,197.13,51.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,204.79,54.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.54" y="-7.25"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="21.554663" y="-7.25"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="32.907387" y="-7.25"> </t年代p一个n> </text> <g> <path d="m 217.33,57.77 27.42,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,225.85,45.89)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,231.35,42.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,245.95,46.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,256.92,43.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,260.77,40.95)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,264.9,54.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,270.95,51.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,275.82,54.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="6.6515961" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,287.98,51.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,292.85,54.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="175.02" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="179.1835" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="185.435" y="0"> 3</t年代p一个n> <tspan style="font-size: 12.50px; " x="191.68649" y="0"> )</t年代p一个n> </text> </g> </g> </svg></span>在哪里<年代vg height="10.925" id="M90" style="vertical-align:-3.13504pt;width:13.1px;" version="1.1" viewbox="0 0 13.1 10.925" width="13.1" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.925)"> <g transform="translate(72,-63.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-66.45,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> </g> </g> </svg>和<年代vg height="10.925" id="M91" style="vertical-align:-3.13504pt;width:13.1px;" version="1.1" viewbox="0 0 13.1 10.925" width="13.1" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.925)"> <g transform="translate(72,-63.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-66.45,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> </g> </g> </svg>由curve-labeled表面封闭的单箭头<年代vg height="14.6" id="M92" style="vertical-align:-3.13504pt;width:51.137501px;" version="1.1" viewbox="0 0 51.137501 14.6" width="51.137501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="13.678282" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="25.718672" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-40.17,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-35.3,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n> </text> </g> </g> </svg>和双箭头<年代vg height="14.6" id="M93" style="vertical-align:-3.13504pt;width:51.137501px;" version="1.1" viewbox="0 0 51.137501 14.6" width="51.137501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="13.678282" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="25.718672" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-40.17,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-35.3,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n> </text> </g> </g> </svg>显示在图<一个href="//www.newsama.com/journals/ijap/2012/956431/fig2/" target="_blank">2</一个>,<我>α</我>是免费的参数,我们使用<年代vg height="11.0375" id="M94" style="vertical-align:-0.27588pt;width:48.299999px;" version="1.1" viewbox="0 0 48.299999 11.0375" width="48.299999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0375)"> <g transform="translate(72,-63.17)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="10.515023" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="22.555412" y="0"> 9</t年代p一个n> <tspan style="font-size: 12.50px; " x="28.806911" y="0"> /</t年代p一个n> <tspan style="font-size: 12.50px; " x="32.282745" y="0"> 8</t年代p一个n> </text> </g> </g> </svg>在我们下面的数值例子为了tobeconsistent高阶空间方向的差异。此外,平均电导率可以以类似的方式处理,这消耗CPU时间在初始过程精制亚晶胞模型。</p> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-c87b968a8a5089762becb9864749e62d"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/ijap/volume-2012/956431/figures/956431.fig.001a.jpg"> <br> <strong>(一)</年代trong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/ijap/volume-2012/956431/figures/956431.fig.001b.jpg"> <br> <strong>(b)</年代trong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-c87b968a8a5089762becb9864749e62d partial-carousel-thumbnail"> <button aria-label="Slide to (a) " class="partial-carousel-dot"><img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/ijap/volume-2012/956431/thumbnails/956431.fig.001a_th.jpg"><br><strong>(一)</年代trong></button> <button aria-label="Slide to (b) " class="partial-carousel-dot"><img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/ijap/volume-2012/956431/thumbnails/956431.fig.001b_th.jpg"><br><strong>(b)</年代trong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-c87b968a8a5089762becb9864749e62d partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图1</年代p一个n> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijap/2012/956431/fig1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> <tbody> <tr> <td>对比两种近似。(一)<年代vg height="13.8125" id="M95" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 23.237499 13.8125" width="23.237499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.017,0,0,-.017,.062,13.55)"> <path d="M391 364q0 -28 -20.5 -53.5t-50 -43.5t-70 -34t-73.5 -25t-68 -17v-29q0 -48 20 -81t65 -33q73 0 157 76l16 -23q-107 -113 -221 -113q-21 0 -40.5 6.5t-39 22t-31.5 47t-12 75.5q0 69 33.5 139.5t95.5 114.5q77 55 143 55q42 0 69 -24.5t27 -59.5zM313 350 q0 26 -14.5 40.5t-37.5 14.5q-32 0 -44 -7q-82 -46 -104 -175q200 49 200 127z" id="x1D452"></path> </g> <g transform="matrix(.012,0,0,-.012,7.1,5.388)"> <path d="M535 230h-483v50h483v-50z" id="x2212"></path> </g> <g transform="matrix(.012,0,0,-.012,14.085,5.388)"> <path d="M689 332q0 -81 -40 -161.5t-103.5 -131.5t-127.5 -51q-32 0 -58.5 16t-40.5 46q-70 -62 -139 -62q-45 0 -77.5 30t-32.5 86q0 8 7 52q11 77 45 187q6 19 6 34q0 6 -7 6q-24 0 -78 -64l-20 23q32 48 73 77t78 29q32 0 32 -43q0 -30 -12 -73q-27 -95 -38 -152 q-8 -44 -8 -58q0 -77 68 -77q31 0 60 33.5t39 77.5l62 260l75 16l5 -6l-63 -246q-8 -29 -8 -58q0 -77 68 -77q66 0 116 75.5t50 194.5q0 43 -12 57q-11 12 -11 24q0 19 15 35.5t34 16.5q18 0 30.5 -34.5t12.5 -81.5z" id="x1D464"></path> </g> </svg>和(b)<年代vg height="16.5" id="M96" style="vertical-align:-2.3205pt" version="1.1" viewbox="0 0 79.800003 16.5" width="79.800003" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.017,0,0,-.017,.062,13.55)"> <path d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" id="x28"></path> </g> <g transform="matrix(.017,0,0,-.017,5.944,13.55)"> <path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path> </g> <g transform="matrix(.017,0,0,-.017,17.877,13.55)"> <path d="M535 230h-483v50h483v-50z" id="x2212"></path> </g> <g transform="matrix(.017,0,0,-.017,31.629,13.55)"> <path d="M391 364q0 -28 -20.5 -53.5t-50 -43.5t-70 -34t-73.5 -25t-68 -17v-29q0 -48 20 -81t65 -33q73 0 157 76l16 -23q-107 -113 -221 -113q-21 0 -40.5 6.5t-39 22t-31.5 47t-12 75.5q0 69 33.5 139.5t95.5 114.5q77 55 143 55q42 0 69 -24.5t27 -59.5zM313 350 q0 26 -14.5 40.5t-37.5 14.5q-32 0 -44 -7q-82 -46 -104 -175q200 49 200 127z" id="x1D452"></path> </g> <g transform="matrix(.012,0,0,-.012,38.675,5.388)"> <path d="M535 230h-483v50h483v-50z" id="x2212"></path> </g> <g transform="matrix(.012,0,0,-.012,45.66,5.388)"> <path d="M689 332q0 -81 -40 -161.5t-103.5 -131.5t-127.5 -51q-32 0 -58.5 16t-40.5 46q-70 -62 -139 -62q-45 0 -77.5 30t-32.5 86q0 8 7 52q11 77 45 187q6 19 6 34q0 6 -7 6q-24 0 -78 -64l-20 23q32 48 73 77t78 29q32 0 32 -43q0 -30 -12 -73q-27 -95 -38 -152 q-8 -44 -8 -58q0 -77 68 -77q31 0 60 33.5t39 77.5l62 260l75 16l5 -6l-63 -246q-8 -29 -8 -58q0 -77 68 -77q66 0 116 75.5t50 194.5q0 43 -12 57q-11 12 -11 24q0 19 15 35.5t34 16.5q18 0 30.5 -34.5t12.5 -81.5z" id="x1D464"></path> </g> <g transform="matrix(.017,0,0,-.017,54.75,13.55)"> <path d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" id="x29"></path> </g> <g transform="matrix(.017,0,0,-.017,60.632,13.55)"> <path d="M368 703l-264 -866h-60l265 866h59z" id="x2F"></path> </g> <g transform="matrix(.017,0,0,-.017,67.635,13.55)"> <path d="M689 332q0 -81 -40 -161.5t-103.5 -131.5t-127.5 -51q-32 0 -58.5 16t-40.5 46q-70 -62 -139 -62q-45 0 -77.5 30t-32.5 86q0 8 7 52q11 77 45 187q6 19 6 34q0 6 -7 6q-24 0 -78 -64l-20 23q32 48 73 77t78 29q32 0 32 -43q0 -30 -12 -73q-27 -95 -38 -152 q-8 -44 -8 -58q0 -77 68 -77q31 0 60 33.5t39 77.5l62 260l75 16l5 -6l-63 -246q-8 -29 -8 -58q0 -77 68 -77q66 0 116 75.5t50 194.5q0 43 -12 57q-11 12 -11 24q0 19 15 35.5t34 16.5q18 0 30.5 -34.5t12.5 -81.5z" id="x1D464"></path> </g> </svg>。</td> </tr> </tbody> </table> </div> </div> </div> </div> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-d6eedc7462cacbeca72aa64fee58413d"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2012/956431/figures/956431.fig.002.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-d6eedc7462cacbeca72aa64fee58413d partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2012/956431/thumbnails/956431.fig.002_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-d6eedc7462cacbeca72aa64fee58413d partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图2</年代p一个n> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijap/2012/956431/fig2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> <tbody> <tr> <td>亚晶胞技术指定交货场计算的<年代vg height="15.0875" id="M97" style="vertical-align:-2.3205pt" version="1.1" viewbox="0 0 49.775002 15.0875" width="49.775002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.017,0,0,-.017,.062,12.138)"> <path d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" id="x28"></path> </g> <g transform="matrix(.017,0,0,-.017,5.944,12.138)"> <path d="M456 178h-96v-72q0 -51 12.5 -62.5t72.5 -16.5v-27h-256v27q65 5 78 17t13 62v72h-260v28q182 271 300 426h40v-407h96v-47zM280 225v295h-2q-107 -148 -196 -295h198z" id="x34"></path> </g> <g transform="matrix(.017,0,0,-.017,14.103,12.138)"> <path d="M95 130q31 0 61 -30t30 -78q0 -53 -38 -87.5t-93 -51.5l-11 29q77 31 77 85q0 26 -17.5 43t-44.5 24q-4 0 -8.5 6.5t-4.5 17.5q0 18 15 30t34 12z" id="x2C"></path> </g> <g transform="matrix(.017,0,0,-.017,26.462,12.138)"> <path d="M998 650l-8 -28q-71 -4 -86 -16t-22 -69l-50 -397q-3 -28 -4.5 -44t2 -29t6.5 -18.5t17 -10.5t24.5 -6.5t37.5 -3.5l-8 -28h-271l7 28q63 6 78 22t25 90l60 415h-2l-353 -552h-23l-130 536h-2l-70 -254q-44 -158 -47 -188q-5 -38 9 -51t71 -18l-6 -28h-241l8 28 q45 4 67 18.5t35 45.5q16 38 74 233l52 173q24 79 11.5 98t-89.5 26l6 28h177l136 -508l337 508h172z" id="x1D440"></path> </g> <g transform="matrix(.017,0,0,-.017,43.817,12.138)"> <path d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" id="x29"></path> </g> </svg>计划。</td> </tr> </tbody> </table> </div> </div> </div> </div> <h5 id="sec3.2">3.2。提出的稳定(4米)计划</h5> <p>传统的方法是使用傅里叶模式分析提出的稳定<年代vg height="13.45" id="M98" style="vertical-align:-2.21957pt;width:43.174999px;" version="1.1" viewbox="0 0 43.174999 13.45" width="43.174999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 4</t年代p一个n> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="17.704248" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="30.269764" y="0"> )</t年代p一个n> </text> </g> </g> </svg>计划。为清晰起见,以一维开始讨论<我>z</我>导演,<我>x</我>极化TEM波。方程可以写成<年代p一个nclass="equation" id="EEq18"> <svg height="69.512497" id="M99" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 69.512497" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,69.5125)"> <g transform="translate(72,-16.39)"> <text transform="matrix(1,0,0,-1,115.25,48.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <g> <path d="m 113.3,44.19 10.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,113.3,32.32)"> <tspan style="font-size: 12.50px; " x="13.58" y="0.99000001"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="23.68" y="-20.610001"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="6.3765302" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,147.9,49.8)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,137.74,30.46)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,146.67,27.33)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,152.74,31.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="13.57" y="-9.7399998"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="25.610001" y="-28.049999"> ⎛</t年代p一个n> <tspan style="font-size: 12.50px; " x="25.610001" y="-17.299999"> ⎜</t年代p一个n> <tspan style="font-size: 12.50px; " x="25.610001" y="-6.5500002"> ⎜</t年代p一个n> <tspan style="font-size: 12.50px; " x="25.610001" y="4.1999998"> ⎜</t年代p一个n> <tspan style="font-size: 12.50px; " x="25.610001" y="14.89"> ⎝</t年代p一个n> <tspan style="font-size: 12.50px; " x="79.879997" y="-31.440001"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="54.639999" y="-24.18"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="69.431046" y="-24.18"> −</t年代p一个n> </text> <g> <path d="m 231.94,58.64 7.61,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,231.94,46.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="13.13" y="-16.01"> </t年代p一个n> </text> <g> <path d="m 241.95,58.64 12.62,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,241.95,46.76)"> <tspan style="font-size: 12.50px; " x="-57.970001" y="20.66"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="-48.209999" y="13.41"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="6.3765302" y="0"> </t年代p一个n> </text> <g> <path d="m 193.74,29.22 6.25,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,193.84,17.34)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="11.66" y="-16.01"> </t年代p一个n> </text> <g> <path d="m 202.38,29.22 12.63,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,202.38,17.34)"> <tspan style="font-size: 12.50px; " x="33.470001" y="-8.7600002"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="53.389999" y="-42.040001"> ⎞</t年代p一个n> <tspan style="font-size: 12.50px; " x="53.389999" y="-31.290001"> ⎟</t年代p一个n> <tspan style="font-size: 12.50px; " x="53.389999" y="-20.540001"> ⎟</t年代p一个n> <tspan style="font-size: 12.50px; " x="53.389999" y="-9.79"> ⎟</t年代p一个n> <tspan style="font-size: 12.50px; " x="53.389999" y="0.89999998"> ⎠</t年代p一个n> <tspan style="font-size: 12.50px; " x="61.099998" y="-13.99"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="71.199997" y="-35.59"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="6.3765302" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,284.5,49.8)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,274.34,30.46)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,283.27,27.33)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,289.34,31.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="12.18" y="-9.7399998"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="178.53" y="-9.7399998"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="182.6935" y="-9.7399998"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="188.94499" y="-9.7399998"> 4</t年代p一个n> <tspan style="font-size: 12.50px; " x="195.1965" y="-9.7399998"> )</t年代p一个n> </text> </g> </g> </svg></span>该领域的组件<年代vg height="7.1374998" id="M100" style="vertical-align:-0.10033pt;width:7.8874998px;" version="1.1" viewbox="0 0 7.8874998 7.1374998" width="7.8874998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>时间步长被指示为<年代p一个nclass="equation" id="EEq19"> <svg height="58.825001" id="M101" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 58.825001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,58.825)"> <g transform="translate(72,-24.94)"> <text transform="matrix(1,0,0,-1,126.15,35.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="10.11" y="-21.59"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,147.17,54.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,137.01,34.73)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,145.94,31.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,152.01,35.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="10.1" y="-27.32"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="10.1" y="-16.66"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="10.1" y="-5.9899998"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="10.1" y="4.6700001"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="10.1" y="7.8400002"> |</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,164.61,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="42.98"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3672481" y="42.98"> =</t年代p一个n> <tspan style="font-size: 8.75px; " x="10.362368" y="42.98"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,183.69,45.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.04" y="9.7299995"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="22.139999" y="-12.19"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,217.87,62.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="-1.12" y="9.2799997"> 0</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,225.5,57.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</t年代p一个n> <tspan style="font-size: 12.50px; " x="6.3515239" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,237.42,62.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,246.82,60.33)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,250.44,62.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ⋅</t年代p一个n> <tspan style="font-size: 8.75px; " x="2.503072" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,257.69,60.33)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,261.3,62.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="4.7435842" y="0"> Δ</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,272.37,60.33)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,207.01,32.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,216.69,37.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="-0.75" y="9.29"> 0</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,224.32,32.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</t年代p一个n> <tspan style="font-size: 12.50px; " x="6.3390212" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,236.23,37.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,245.63,35.72)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,249.26,37.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ⋅</t年代p一个n> <tspan style="font-size: 8.75px; " x="2.503072" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,256.5,35.72)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,260.12,37.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="4.7435842" y="0"> Δ</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,271.18,35.72)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,276.48,35.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="12.19" y="-9.7299995"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="191.39" y="-9.7299995"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="195.5535" y="-9.7299995"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="201.80499" y="-9.7299995"> 5</t年代p一个n> <tspan style="font-size: 12.50px; " x="208.0565" y="-9.7299995"> )</t年代p一个n> </text> </g> </g> </svg></span>在这里,<年代vg height="14.625" id="M102" style="vertical-align:-3.25793pt;width:14.675px;" version="1.1" viewbox="0 0 14.675 14.625" width="14.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-65.17,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>空间频率在吗<我>z</我>方向。替换(<一个href="#EEq19">15</一个>)(<一个href="#EEq12">9</一个>),我们得到<年代p一个nclass="equation" id="EEq20"> <svg height="94.425003" id="M103" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 94.425003" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,94.425)"> <g transform="translate(72,3.54)"> <text transform="matrix(1,0,0,-1,68.75,63.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> </t年代p一个n> </text> <g> <path d="m 68.75,58.89 15.93,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,70.4,47.02)"> <tspan style="font-size: 12.50px; " x="15.48" y="-15.67"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="15.48" y="-5"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="15.48" y="-1.84"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,88.38,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="21.879999"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,67.75,12.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,80.06,28.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="8.7957602" y="0"> /</t年代p一个n> <tspan style="font-size: 8.75px; " x="11.228816" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,79.79,6.26)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,80.75,-0.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> =</t年代p一个n> <tspan style="font-size: 8.75px; " x="9.8459997" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,95.94,12.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,101.98,9.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,107.53,20.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,113.09,25.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,122.49,22.88)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,126.11,25.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="6.765296" y="0"> −</t年代p一个n> <tspan style="font-size: 8.75px; " x="12.760416" y="0"> 1</t年代p一个n> <tspan style="font-size: 8.75px; " x="17.136415" y="0"> /</t年代p一个n> <tspan style="font-size: 8.75px; " x="19.569471" y="0"> 2</t年代p一个n> <tspan style="font-size: 8.75px; " x="23.945473" y="0"> )</t年代p一个n> <tspan style="font-size: 8.75px; " x="26.859888" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,157.72,22.88)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,161.33,25.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Δ</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,167.65,22.88)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,174.55,20.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,191.45,25.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,194.86,22.88)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,198.48,25.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="6.765296" y="0"> −</t年代p一个n> <tspan style="font-size: 8.75px; " x="12.760416" y="0"> 1</t年代p一个n> <tspan style="font-size: 8.75px; " x="17.136415" y="0"> /</t年代p一个n> <tspan style="font-size: 8.75px; " x="19.569471" y="0"> 2</t年代p一个n> <tspan style="font-size: 8.75px; " x="23.945473" y="0"> )</t年代p一个n> <tspan style="font-size: 8.75px; " x="26.859888" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,230.09,22.88)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,233.7,25.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Δ</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,240.02,22.88)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <g> <path d="m 107.53,15.94 136.61,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,168.89,4.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,177.91,0.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,248.11,12.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</t年代p一个n> <tspan style="font-size: 12.50px; " x="6.3515239" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="14.078378" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="29.244516" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="40.447205" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="52.487595" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,311.52,9.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,320.53,12.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> o</t年代p一个n> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> r</t年代p一个n> <tspan style="font-size: 12.50px; " x="14.578498" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,344.04,9.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,349.35,12.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="118.52" y="-18.290001"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="122.6835" y="-18.290001"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="128.935" y="-18.290001"> 6</t年代p一个n> <tspan style="font-size: 12.50px; " x="135.18649" y="-18.290001"> )</t年代p一个n> </text> </g> </g> </svg></span>然后(<一个href="#EEq18">14</一个>)可以写成<年代p一个nclass="equation" id="EEq21"> <svg height="69.512497" id="M104" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 69.512497" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,69.5125)"> <g transform="translate(72,-16.39)"> <text transform="matrix(1,0,0,-1,119.53,48.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <g> <path d="m 117.57,44.19 10.31,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,117.57,32.32)"> <tspan style="font-size: 12.50px; " x="13.59" y="0.99000001"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="25.92" y="-20.92"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,154.4,50.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,144.25,30.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,153.17,27.65)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,161.47,31.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="13.58" y="-9.7399998"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="25.620001" y="-28.049999"> ⎛</t年代p一个n> <tspan style="font-size: 12.50px; " x="25.620001" y="-17.299999"> ⎜</t年代p一个n> <tspan style="font-size: 12.50px; " x="25.620001" y="-6.5500002"> ⎜</t年代p一个n> <tspan style="font-size: 12.50px; " x="25.620001" y="4.1999998"> ⎜</t年代p一个n> <tspan style="font-size: 12.50px; " x="25.620001" y="14.89"> ⎝</t年代p一个n> <tspan style="font-size: 12.50px; " x="75.989998" y="-31.42"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="42.279999" y="-24.17"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="65.535583" y="-24.17"> −</t年代p一个n> </text> <g> <path d="m 236.78,58.62 7.61,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,236.78,46.74)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="8.8100004" y="-8.75"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,251.84,52.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,192.71,26.08)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="9.7600002" y="-7.25"> 1</t年代p一个n> </text> <g> <path d="m 202.47,29.2 6.26,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,202.57,17.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="7.3499999" y="-8.75"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,216.17,22.95)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,238.73,26.08)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="17.969999" y="-33.299999"> ⎞</t年代p一个n> <tspan style="font-size: 12.50px; " x="17.969999" y="-22.549999"> ⎟</t年代p一个n> <tspan style="font-size: 12.50px; " x="17.969999" y="-11.8"> ⎟</t年代p一个n> <tspan style="font-size: 12.50px; " x="17.969999" y="-1.05"> ⎟</t年代p一个n> <tspan style="font-size: 12.50px; " x="17.969999" y="9.6400003"> ⎠</t年代p一个n> <tspan style="font-size: 12.50px; " x="25.68" y="-5.25"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="35.790001" y="-26.85"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,285.43,49.8)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,275.27,30.46)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,284.2,27.33)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,290.27,31.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="177.60001" y="-9.7399998"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="181.7635" y="-9.7399998"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="188.015" y="-9.7399998"> 7</t年代p一个n> <tspan style="font-size: 12.50px; " x="194.26649" y="-9.7399998"> )</t年代p一个n> </text> </g> </g> </svg></span>与<年代p一个nclass="equation" id="eq6"> <svg height="50.924999" id="M105" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 50.924999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,50.925)"> <g transform="translate(72,-31.26)"> <text transform="matrix(1,0,0,-1,110.73,47.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,116.98,44.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,125.32,47.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,137.63,63.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="8.7957602" y="0"> /</t年代p一个n> <tspan style="font-size: 8.75px; " x="11.228816" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,137.35,41.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,138.32,33.89)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> =</t年代p一个n> <tspan style="font-size: 8.75px; " x="9.8459997" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,153.51,47.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,159.55,44.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,165.09,54.87)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,170.65,59.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,180.05,57.68)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,183.68,59.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="6.765296" y="0"> −</t年代p一个n> <tspan style="font-size: 8.75px; " x="12.760416" y="0"> 1</t年代p一个n> <tspan style="font-size: 8.75px; " x="17.136415" y="0"> /</t年代p一个n> <tspan style="font-size: 8.75px; " x="19.569471" y="0"> 2</t年代p一个n> <tspan style="font-size: 8.75px; " x="23.945473" y="0"> )</t年代p一个n> <tspan style="font-size: 8.75px; " x="26.859888" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,215.28,57.68)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,218.9,59.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Δ</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,225.22,57.68)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,232.11,54.87)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,249.02,59.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,252.42,57.68)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,256.05,59.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="6.765296" y="0"> −</t年代p一个n> <tspan style="font-size: 8.75px; " x="12.760416" y="0"> 1</t年代p一个n> <tspan style="font-size: 8.75px; " x="17.136415" y="0"> /</t年代p一个n> <tspan style="font-size: 8.75px; " x="19.569471" y="0"> 2</t年代p一个n> <tspan style="font-size: 8.75px; " x="23.945473" y="0"> )</t年代p一个n> <tspan style="font-size: 8.75px; " x="26.859888" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,287.65,57.68)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,291.27,59.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Δ</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,297.59,57.68)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <g> <path d="m 165.09,50.74 136.61,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,226.45,38.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,235.48,35.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,302.9,47.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="164.97" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="169.1335" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="175.38499" y="0"> 8</t年代p一个n> <tspan style="font-size: 12.50px; " x="181.63651" y="0"> )</t年代p一个n> </text> </g> </g> </svg></span></p> <p>应用<年代vg height="13.45" id="M106" style="vertical-align:-2.21957pt;width:43.174999px;" version="1.1" viewbox="0 0 43.174999 13.45" width="43.174999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 4</t年代p一个n> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="17.704248" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="30.269764" y="0"> )</t年代p一个n> </text> </g> </g> </svg>计划(<一个href="#EEq21">17</一个>),呢关系可以表示为<年代p一个nclass="equation" id="EEq22"> <svg height="50.4375" id="M107" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 50.4375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,50.4375)"> <g transform="translate(72,-31.65)"> <text transform="matrix(1,0,0,-1,150.19,38.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="10.11" y="-22.059999"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,172.34,66.03)"> <tspan style="font-size: 8.75px; " x="-1.13" y="9.5699997"> 0</t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> +</t年代p一个n> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,161.48,36.4)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,171.15,41.4)"> <tspan style="font-size: 8.75px; " x="-0.75" y="9.5699997"> 0</t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> +</t年代p一个n> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,187.56,38.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="36.689999" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="46.799999" y="-21.92"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="13.57" y="-9.7299995"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="25.597885" y="-9.7299995"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,246.4,65.89)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="-1.13" y="9.29"> 0</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,235.54,38.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,245.22,43.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="-0.75" y="9.2799997"> 0</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,251.25,38.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="12.18" y="-9.7299995"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="216.62" y="-9.7299995"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="220.78349" y="-9.7299995"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="227.035" y="-9.7299995"> 9</t年代p一个n> <tspan style="font-size: 12.50px; " x="233.2865" y="-9.7299995"> )</t年代p一个n> </text> </g> </g> </svg></span>在哪里<年代p一个nclass="equation" id="EEq23"> <svg height="61.424999" id="M108" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 61.424999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,61.425)"> <g transform="translate(72,-22.86)"> <text transform="matrix(1,0,0,-1,115.16,44.3)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="11.590281" y="0"> =</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,146.12,60.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,138.8,37.74)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,141.73,30.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="2.7831359" y="0"> =</t年代p一个n> <tspan style="font-size: 8.75px; " x="8.7782564" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,159.91,57.24)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⎛</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="10.75"> ⎜</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="21.5"> ⎜</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="32.189999"> ⎝</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.6199999" y="25.450001"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="15.38" y="16.18"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="24.719999" y="-5.96"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="56.040016" y="-5.96"> 0</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,181.54,37.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,186.41,41.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,193.06,37.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,196.52,41.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,205.55,37.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <g> <path d="m 175.29,34.92 33.49,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,189.01,23.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="26.950001" y="-8.75"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="33.200001" y="-34.200001"> ⎞</t年代p一个n> <tspan style="font-size: 12.50px; " x="33.200001" y="-23.450001"> ⎟</t年代p一个n> <tspan style="font-size: 12.50px; " x="33.200001" y="-12.7"> ⎟</t年代p一个n> <tspan style="font-size: 12.50px; " x="33.200001" y="-2.01"> ⎠</t年代p一个n> <tspan style="font-size: 12.50px; " x="40.91" y="-34.200001"> ⎛</t年代p一个n> <tspan style="font-size: 12.50px; " x="40.91" y="-23.450001"> ⎜</t年代p一个n> <tspan style="font-size: 12.50px; " x="40.91" y="-12.7"> ⎜</t年代p一个n> <tspan style="font-size: 12.50px; " x="40.91" y="-2.01"> ⎝</t年代p一个n> <tspan style="font-size: 12.50px; " x="68.519997" y="-37.91"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="46.529999" y="-28.65"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="58.757935" y="-28.65"> −</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,263.79,57.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,268.65,60.95)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,273.84,57.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,277.3,60.95)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,286.32,57.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <g> <path d="m 257.53,54.82 32.03,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,269.74,42.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="21.02" y="-14.3"> ⎞</t年代p一个n> <tspan style="font-size: 12.50px; " x="21.02" y="-3.55"> ⎟</t年代p一个n> <tspan style="font-size: 12.50px; " x="21.02" y="7.1999998"> ⎟</t年代p一个n> <tspan style="font-size: 12.50px; " x="21.02" y="17.889999"> ⎠</t年代p一个n> <tspan style="font-size: 12.50px; " x="-34.200001" y="13.71"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="-3.605159" y="13.71"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="28.73" y="-1.36"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="198.13" y="-1.36"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="202.2935" y="-1.36"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="208.545" y="-1.36"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="214.79649" y="-1.36"> )</t年代p一个n> </text> </g> </g> </svg></span>求解特征值,我们可以获得<年代p一个nclass="equation" id="EEq24"> <svg height="40.012501" id="M109" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 40.012501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,40.0125)"> <g transform="translate(72,-39.99)"> <text transform="matrix(1,0,0,-1,129.56,48.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,136.33,45.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ,</t年代p一个n> <tspan style="font-size: 8.75px; " x="6.5640001" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,151.24,48.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="13.23" y="-9.2600002"> t</t年代p一个n> <tspan style="font-size: 12.50px; " x="16.705833" y="-9.2600002"> r</t年代p一个n> <tspan style="font-size: 12.50px; " x="25.790001" y="-9.2700005"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="29.953499" y="-9.2700005"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="38.943157" y="-9.2700005"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="45.88232" y="-9.2700005"> ±</t年代p一个n> <tspan style="font-size: 12.50px; " x="57.235046" y="-9.2700005"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,213.34,54.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,218.22,58.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> √</t年代p一个n> </text> <g> <path d="m 229.82,70.71 53.05,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,229.82,58.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 4</t年代p一个n> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="20.367388" y="0"> t</t年代p一个n> <tspan style="font-size: 12.50px; " x="23.843222" y="0"> r</t年代p一个n> <tspan style="font-size: 12.50px; " x="30.85" y="-0.0099999998"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="35.0135" y="-0.0099999998"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="44.003155" y="-0.0099999998"> )</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,277.99,63.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> <g> <path d="m 164.47,51.92 118.4,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,220.54,40.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="63.52" y="-8.75"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="247.33" y="-8.75"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="251.4935" y="-8.75"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="257.745" y="-8.75"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="263.99649" y="-8.75"> )</t年代p一个n> </text> </g> </g> </svg></span>在哪里<年代p一个nclass="equation" id="EEq25"> <svg height="150.33749" id="M110" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 150.33749" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,150.3375)"> <g transform="translate(72,48.27)"> <text transform="matrix(1,0,0,-1,81.15,47.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> t</t年代p一个n> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> r</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.553012" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="16.716511" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="25.718672" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="33.358006" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="45.385891" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="54.42556" y="0"> +</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,152.81,63.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,146.92,40.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,148.42,33.78)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="2.7831359" y="0"> =</t年代p一个n> <tspan style="font-size: 8.75px; " x="8.7782564" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,163.08,47.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,169.23,44.39)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,172.68,45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.52"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="10.013499" y="-2.52"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="16.064951" y="-2.52"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="23.679277" y="-2.52"> )</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,200.53,52.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,211.4,47.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,220.42,52.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="8.2700005"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,225.3,47.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,231.55,52.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="8.1199999"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,236.42,45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,242.28,55.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,245.73,47.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="-144.3" y="37.450001"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,107.58,6.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,114.51,10.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="55.419998" y="6.5500002"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,126.55,-3.78)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ≤</t年代p一个n> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,139.64,-5.96)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,143.27,-3.78)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ≤</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,152.67,-5.96)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,156.29,-3.78)"> <tspan style="font-size: 8.75px; " x="0" y="0"> <</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,165.01,-5.96)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,168.63,-3.78)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ≤</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,178.03,-5.96)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,181.65,-3.78)"> <tspan style="font-size: 8.75px; " x="0" y="0"> <</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> ⋯</t年代p一个n> <tspan style="font-size: 8.75px; " x="14.099472" y="0"> <</t年代p一个n> <tspan style="font-size: 8.75px; " x="20.094591" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,204.47,-5.96)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,207.08,-3.78)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ≤</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,216.48,-5.96)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,219.09,-3.78)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ≤</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 5</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,229.46,10.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,234.65,6.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,237.37,4.75)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,241.5,10.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,248.15,6.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,251.55,4.75)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,255.68,10.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,260.86,6.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,263.59,4.75)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,267.71,10.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,274.36,6.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,277.76,4.75)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,283.97,10.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋯</t年代p一个n> <tspan style="font-size: 12.50px; " x="15.741277" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,304.9,6.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,307.63,4.75)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,310.74,10.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,317.39,6.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,320.79,4.75)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,123.78,-29.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="54.720001" y="6.5500002"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,135.12,-43.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ≤</t年代p一个n> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,148.21,-45.68)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,151.84,-43.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> <</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,161.24,-45.68)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,164.86,-43.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ≤</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,173.58,-45.68)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,177.2,-43.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> <</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,186.6,-45.68)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,190.23,-43.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ≤</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> ⋯</t年代p一个n> <tspan style="font-size: 8.75px; " x="14.099472" y="0"> ≤</t年代p一个n> <tspan style="font-size: 8.75px; " x="20.094591" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,213.04,-45.68)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,215.66,-43.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> <</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,225.06,-45.68)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,227.67,-43.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ≤</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 5</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,238.04,-29.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,244.69,-32.78)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,247.41,-34.97)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,251.53,-29.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,256.72,-32.78)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,260.13,-34.97)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,264.25,-29.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,270.9,-32.78)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,273.62,-34.97)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,277.74,-29.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,282.93,-32.78)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,286.34,-34.97)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,292.54,-29.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋯</t年代p一个n> <tspan style="font-size: 12.50px; " x="15.741277" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,314.94,-32.78)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,317.66,-34.97)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,320.77,-29.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,325.96,-32.78)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,329.37,-34.97)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,332.47,-29.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="135.39999" y="-38.400002"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="139.56349" y="-38.400002"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="145.815" y="-38.400002"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="152.0665" y="-38.400002"> )</t年代p一个n> </text> </g> </g> </svg></span>我们可以得出这样的结论:<年代vg height="16.137501" id="M111" style="vertical-align:-4.37273pt;width:56.337502px;" version="1.1" viewbox="0 0 56.337502 16.137501" width="56.337502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.1375)"> <g transform="translate(72,-59.09)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="2.5006001" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-62.69,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ,</t年代p一个n> <tspan style="font-size: 8.75px; " x="6.5640001" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-51.25,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.9764342" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="18.00432" y="0"> 1</t年代p一个n> </text> </g> </g> </svg>如果<年代vg height="13.45" id="M112" style="vertical-align:-2.21957pt;width:72.449997px;" version="1.1" viewbox="0 0 72.449997 13.45" width="72.449997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.576098" y="0"> t</t年代p一个n> <tspan style="font-size: 12.50px; " x="8.0519323" y="0"> r</t年代p一个n> <tspan style="font-size: 12.50px; " x="17.12911" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="21.292608" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="29.419559" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="33.583057" y="0"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="39.55949" y="0"> ≤</t年代p一个n> <tspan style="font-size: 12.50px; " x="51.59988" y="0"> 2</t年代p一个n> </text> </g> </g> </svg>,该计划是稳定的。此外,在这种情况下,方案无耗散。</p> <p>在三维(3 d)情况下,连续时间离散空间麦克斯韦方程可以写成<年代p一个nclass="equation" id="EEq27"> <svg height="147.22501" id="M113" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 147.22501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,147.225)"> <g transform="translate(72,45.78)"> <text transform="matrix(1,0,0,-1,56.61,56.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <g> <path d="m 54.66,52.73 10.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,54.66,40.85)"> <tspan style="font-size: 12.50px; " x="13.58" y="0.98000002"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="23.68" y="-20.610001"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="24.370001" y="1.86"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="33.41" y="0.98000002"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="2.27" y="54.57"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="14.31" y="30.879999"> ⎛</t年代p一个n> <tspan style="font-size: 12.50px; " x="14.31" y="41.630001"> ⎜</t年代p一个n> <tspan style="font-size: 12.50px; " x="14.31" y="52.380001"> ⎜</t年代p一个n> <tspan style="font-size: 12.50px; " x="14.31" y="63.139999"> ⎜</t年代p一个n> <tspan style="font-size: 12.50px; " x="14.31" y="73.889999"> ⎜</t年代p一个n> <tspan style="font-size: 12.50px; " x="14.31" y="84.580002"> ⎝</t年代p一个n> <tspan style="font-size: 12.50px; " x="148.34" y="23.15"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="6.3765302" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="74.639999" y="33.889999"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="138.58" y="33.889999"> −</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,209.25,14.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,214.56,17.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,220.12,14.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,228.21,17.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,245.81,14.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,250.65,17.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,256.21,14.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,263.83,17.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,281.42,14.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,286.29,17.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,291.85,14.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <g> <path d="m 203,10.08 93.72,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,246.05,-1.8)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="54.639999" y="-8.7600002"> ×</t年代p一个n> <tspan style="font-size: 12.50px; " x="-167.27" y="11.8"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,85.03,-16.72)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,90.34,-13.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,95.91,-16.72)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,104,-13.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,121.59,-16.72)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,126.43,-13.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,132,-16.72)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,139.61,-13.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,157.21,-16.72)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,162.07,-13.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,167.64,-16.72)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <g> <path d="m 78.78,-21.21 93.72,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,122.62,-33.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="197.82001" y="-43.060001"> ⎞</t年代p一个n> <tspan style="font-size: 12.50px; " x="197.82001" y="-32.310001"> ⎟</t年代p一个n> <tspan style="font-size: 12.50px; " x="197.82001" y="-21.559999"> ⎟</t年代p一个n> <tspan style="font-size: 12.50px; " x="197.82001" y="-10.8"> ⎟</t年代p一个n> <tspan style="font-size: 12.50px; " x="197.82001" y="-0.050000001"> ⎟</t年代p一个n> <tspan style="font-size: 12.50px; " x="197.82001" y="10.64"> ⎠</t年代p一个n> <tspan style="font-size: 12.50px; " x="205.53" y="-9.6300001"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="215.63" y="-31.23"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="216.33" y="-8.7600002"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="225.36" y="-9.6300001"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="237.55" y="-19.370001"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="53.860001" y="-8.75"> ×</t年代p一个n> <tspan style="font-size: 12.50px; " x="126.61" y="-8.75"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="345.25" y="-43.07"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="349.41351" y="-43.07"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="355.66501" y="-43.07"> 3</t年代p一个n> <tspan style="font-size: 12.50px; " x="361.9165" y="-43.07"> )</t年代p一个n> </text> </g> </g> </svg></span>考虑<年代vg height="19.674999" id="M114" style="vertical-align:-4.74141pt;width:115.3125px;" version="1.1" viewbox="0 0 115.3125 19.674999" width="115.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.675)"> <g transform="translate(72,-56.26)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-61.54,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="8.1199999"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-53.44,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-35.85,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="8.1199999"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-28.2,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-10.6,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="8.1199999"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-5.73,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> <</t年代p一个n> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> 0</t年代p一个n> </text> </g> </g> </svg>,(<一个href="#EEq27">23</一个>在张量形式)可以改写<年代p一个nclass="equation" id="EEq28"> <svg height="162.47501" id="M115" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 162.47501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,162.475)"> <g transform="translate(72,57.98)"> <text transform="matrix(1,0,0,-1,58.94,56.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <g> <path d="m 56.99,52.73 10.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,56.99,40.85)"> <tspan style="font-size: 12.50px; " x="13.58" y="0.98000002"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="23.68" y="-20.610001"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="24.370001" y="1.86"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="33.41" y="0.98000002"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="2.27" y="60.669998"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="14.31" y="31.370001"> ⎛</t年代p一个n> <tspan style="font-size: 12.50px; " x="14.31" y="42.200001"> ⎜</t年代p一个n> <tspan style="font-size: 12.50px; " x="14.31" y="53.029999"> ⎜</t年代p一个n> <tspan style="font-size: 12.50px; " x="14.31" y="63.860001"> ⎜</t年代p一个n> <tspan style="font-size: 12.50px; " x="14.31" y="74.690002"> ⎜</t年代p一个n> <tspan style="font-size: 12.50px; " x="14.31" y="85.519997"> ⎜</t年代p一个n> <tspan style="font-size: 12.50px; " x="14.31" y="96.290001"> ⎝</t年代p一个n> <tspan style="font-size: 12.50px; " x="73.470001" y="46.25"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="140.42999" y="32.740002"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="148.99001" y="36.540001"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="6.3765302" y="0"> </t年代p一个n> </text> <g> <path d="m 219.2,23.3 84.41,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,219.2,8.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="10.65" y="2.51"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="16.5" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,241.95,12.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="7.1700001"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,250.04,8.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,267.64,12.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="7.1599998"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,275.29,8.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,292.88,12.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="7.2399998"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,297.76,5.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <g> <path d="m 197.42,-2.27 106.19,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,246.71,-14.15)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <g> <path d="m 304.81,5.94 9.72,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,304.81,-5.4)"> <tspan style="font-size: 12.50px; " x="-226.69" y="33.939999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="9.727334" y="0"> ⋅</t年代p一个n> </text> <g> <path d="m 91.34,-20.35 84.41,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,91.34,-35.53)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="10.65" y="2.52"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="16.5" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,114.09,-31.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="7.1599998"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,122.18,-35.53)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,139.78,-31.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="7.1500001"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,147.43,-35.53)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,165.02,-31.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="7.2399998"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,169.9,-38.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <g> <path d="m 78.12,-45.92 97.63,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,123.91,-57.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <g> <path d="m 176.94,-37.7 9.73,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,176.94,-49.04)"> <tspan style="font-size: 12.50px; " x="141.17" y="-58.52"> ⎞</t年代p一个n> <tspan style="font-size: 12.50px; " x="141.17" y="-47.689999"> ⎟</t年代p一个n> <tspan style="font-size: 12.50px; " x="141.17" y="-36.860001"> ⎟</t年代p一个n> <tspan style="font-size: 12.50px; " x="141.17" y="-26.030001"> ⎟</t年代p一个n> <tspan style="font-size: 12.50px; " x="141.17" y="-15.2"> ⎟</t年代p一个n> <tspan style="font-size: 12.50px; " x="141.17" y="-4.3699999"> ⎟</t年代p一个n> <tspan style="font-size: 12.50px; " x="141.17" y="6.4000001"> ⎠</t年代p一个n> <tspan style="font-size: 12.50px; " x="148.88" y="-19.48"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="158.98" y="-41.07"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="159.67999" y="-18.610001"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="168.71001" y="-19.48"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="180.89999" y="-29.219999"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="9.727334" y="0"> ⋅</t年代p一个n> <tspan style="font-size: 12.50px; " x="77.099998" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="290.92999" y="-52.919998"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="295.09351" y="-52.919998"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="301.345" y="-52.919998"> 4</t年代p一个n> <tspan style="font-size: 12.50px; " x="307.5965" y="-52.919998"> )</t年代p一个n> </text> </g> </g> </svg></span>在哪里<年代vg height="15.85" id="M116" style="vertical-align:-0.0pt;width:12.2875px;" version="1.1" viewbox="0 0 12.2875 15.85" width="12.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.85)"> <g transform="translate(72,-59.32)"> <g> <path d="m -71.95,70.71 9.73,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>是张量矩阵定义的球形角度(<一个href="#B17">16</一个>]。使用类似的分析,同样的公式(<一个href="#EEq24">21</一个>)获得除了<年代p一个nclass="equation" id="EEq29"> <svg height="48.337502" id="M117" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.337502" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.3375)"> <g transform="translate(72,-33.33)"> <text transform="matrix(1,0,0,-1,90.87,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> t</t年代p一个n> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> r</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.553012" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="16.716511" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="25.718672" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="33.358006" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="45.385891" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="54.42556" y="0"> +</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,161.61,65.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,156.64,43.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,158.14,35.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="2.7831359" y="0"> =</t年代p一个n> <tspan style="font-size: 8.75px; " x="8.7782564" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,174.88,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,181.53,46.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,184.99,47.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.52"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="10.013499" y="-2.52"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="16.064951" y="-2.52"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="23.666775" y="-2.52"> )</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,212.83,54.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,223.7,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,232.73,54.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="8.2700005"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,239.69,47.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,251.79,54.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="8.1199999"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,259.88,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,277.47,54.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="8.1199999"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,285.13,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,302.72,54.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="8.1199999"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,307.6,47.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,319.3,57.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,322.75,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="145.12" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="149.28349" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="155.535" y="0"> 5</t年代p一个n> <tspan style="font-size: 12.50px; " x="161.7865" y="0"> )</t年代p一个n> </text> </g> </g> </svg></span>一般来说,稳定的方案评估Courant-Friedrichs-Levy限制,也就是说,CFLmax,可以表示为<年代p一个nclass="equation" id="EEq30"> <svg height="37.150002" id="M118" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 37.150002" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,37.15)"> <g transform="translate(72,-42.28)"> <text transform="matrix(1,0,0,-1,160.65,54.3)"> <tspan style="font-size: 12.50px; " x="0" y="0"> C</t年代p一个n> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> F</t年代p一个n> <tspan style="font-size: 12.50px; " x="15.291169" y="0"> l</t年代p一个n> <tspan style="font-size: 12.50px; " x="22.930502" y="0"> 米</t年代p一个n> <tspan style="font-size: 12.50px; " x="32.657837" y="0"> 一个</t年代p一个n> <tspan style="font-size: 12.50px; " x="38.209167" y="0"> x</t年代p一个n> <tspan style="font-size: 12.50px; " x="47.924" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="61.16" y="-9.2200003"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="70.187164" y="-9.2200003"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,234.76,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 米</t年代p一个n> <tspan style="font-size: 8.75px; " x="6.8090558" y="0"> 一个</t年代p一个n> <tspan style="font-size: 8.75px; " x="10.694944" y="0"> x</t年代p一个n> </text> <g> <path d="m 221.81,57.42 29.97,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,230.02,45.54)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,236.78,42.42)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,252.98,54.3)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="214.89" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="219.0535" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="225.30499" y="0"> 6</t年代p一个n> <tspan style="font-size: 12.50px; " x="231.5565" y="0"> )</t年代p一个n> </text> </g> </g> </svg></span>在哪里<年代vg height="14.675" id="M119" style="vertical-align:-3.22282pt;width:39.412498px;" version="1.1" viewbox="0 0 39.412498 14.675" width="39.412498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.675)"> <g transform="translate(72,-60.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-59.01,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 米</t年代p一个n> <tspan style="font-size: 8.75px; " x="6.8090558" y="0"> 一个</t年代p一个n> <tspan style="font-size: 8.75px; " x="10.694944" y="0"> x</t年代p一个n> </text> </g> </g> </svg>时间稳定系数,数值时间演化算符不会爆炸<年代vg height="10.8" id="M120" style="vertical-align:-0.11285pt;width:16.299999px;" version="1.1" viewbox="0 0 16.299999 10.8" width="16.299999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8)"> <g transform="translate(72,-63.36)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代p一个n> </text> </g> </g> </svg>可以确定,根据以下的不平等<年代p一个nclass="equation" id="EEq31"> <svg height="156.7" id="M121" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 156.7" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,156.7)"> <g transform="translate(72,53.36)"> <text transform="matrix(1,0,0,-1,94.24,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="10.67"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="21.33"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="32"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="35.16"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="2.5" y="17.59"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.527166" y="17.59"> +</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,123,61.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,117.11,39.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,118.61,32.18)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="2.7831359" y="0"> =</t年代p一个n> <tspan style="font-size: 8.75px; " x="8.7782564" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,135.35,45.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,141.5,42.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,144.96,43.4)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="14.414555" y="-2.51"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="23.441721" y="-2.51"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,172.32,50.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,177.19,43.4)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,183.04,53.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,186.5,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="10.67"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="21.33"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="32"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="35.16"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="39.43" y="16"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="39.43" y="19.16"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="54.869999" y="16"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="54.869999" y="19.16"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.9699998" y="17.59"> ≤</t年代p一个n> <tspan style="font-size: 12.50px; " x="17.997887" y="17.59"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="24.249386" y="17.59"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="41.93" y="17.59"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="50.957165" y="17.59"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="60.849998" y="17.59"> ≤</t年代p一个n> <tspan style="font-size: 12.50px; " x="72.877884" y="17.59"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="81.905052" y="17.59"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,272.33,42.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 米</t年代p一个n> <tspan style="font-size: 8.75px; " x="6.8090558" y="0"> 一个</t年代p一个n> <tspan style="font-size: 8.75px; " x="10.694944" y="0"> x</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,289.35,45.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="-197.2" y="40.939999"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,98.31,1.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,105.24,4.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="55.41" y="6.5500002"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,117.27,-8.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ≤</t年代p一个n> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,130.37,-11.05)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,133.99,-8.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ≤</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,143.39,-11.05)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,147.01,-8.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> <</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,155.73,-11.05)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,159.36,-8.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ≤</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,168.76,-11.05)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,172.38,-8.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> <</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> ⋯</t年代p一个n> <tspan style="font-size: 8.75px; " x="14.099472" y="0"> <</t年代p一个n> <tspan style="font-size: 8.75px; " x="20.094591" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,195.2,-11.05)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,197.81,-8.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ≤</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,207.21,-11.05)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,209.82,-8.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ≤</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 5</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,220.19,4.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,225.38,1.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,228.1,-0.34)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,232.22,4.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,238.87,1.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,242.28,-0.34)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,246.4,4.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,251.59,1.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,254.31,-0.34)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,258.43,4.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,265.08,1.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,268.49,-0.34)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,274.7,4.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋯</t年代p一个n> <tspan style="font-size: 12.50px; " x="13.653276" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,293.55,1.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,296.27,-0.34)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,299.38,4.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,306.03,1.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,309.43,-0.34)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,114.86,-34.75)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="54.720001" y="6.5500002"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,126.2,-48.59)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ≤</t年代p一个n> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,139.29,-50.77)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,142.92,-48.59)"> <tspan style="font-size: 8.75px; " x="0" y="0"> <</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,152.32,-50.77)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,155.94,-48.59)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ≤</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,164.66,-50.77)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,168.28,-48.59)"> <tspan style="font-size: 8.75px; " x="0" y="0"> <</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,177.68,-50.77)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,181.31,-48.59)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ≤</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> ⋯</t年代p一个n> <tspan style="font-size: 8.75px; " x="14.099472" y="0"> ≤</t年代p一个n> <tspan style="font-size: 8.75px; " x="20.094591" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,204.12,-50.77)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,206.74,-48.59)"> <tspan style="font-size: 8.75px; " x="0" y="0"> <</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,216.14,-50.77)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,218.75,-48.59)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ≤</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 5</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,229.12,-34.75)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,235.77,-37.88)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,238.49,-40.06)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,242.61,-34.75)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,247.8,-37.88)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,251.21,-40.06)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,255.33,-34.75)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,261.98,-37.88)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,264.7,-40.06)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,268.82,-34.75)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,274.01,-37.88)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,277.42,-40.06)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,283.62,-34.75)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋯</t年代p一个n> <tspan style="font-size: 12.50px; " x="13.653276" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,303.94,-37.88)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,306.66,-40.06)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,309.77,-34.75)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,314.96,-37.88)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,318.36,-40.06)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,321.47,-34.75)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="146.39999" y="-40.939999"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="150.56349" y="-40.939999"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="156.815" y="-40.939999"> 7</t年代p一个n> <tspan style="font-size: 12.50px; " x="163.0665" y="-40.939999"> )</t年代p一个n> </text> </g> </g> </svg></span>在这里,<年代vg height="14.5875" id="M122" style="vertical-align:-3.22282pt;width:17.075001px;" version="1.1" viewbox="0 0 17.075001 14.5875" width="17.075001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5875)"> <g transform="translate(72,-60.33)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>空间稳定系数,定义为<年代vg height="21.7875" id="M123" style="vertical-align:-3.80836pt;width:147.175px;" version="1.1" viewbox="0 0 147.175 21.7875" width="147.175" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,21.7875)"> <g transform="translate(72,-54.57)"> <text transform="matrix(1,0,0,-1,-71.95,58.42)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-65.19,55.29)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-54.91,58.42)"> <tspan style="font-size: 12.50px; " x="18.290001" y="-0.54000002"> √</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 2</t年代p一个n> </text> <g> <path d="m -25.02,70.71 10.06,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-25.02,58.42)"> <tspan style="font-size: 12.50px; " x="25.709999" y="0.029999999"> ∑</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="12.840581" y="0"> ×</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,12.11,64.65)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="8.7957602" y="0"> /</t年代p一个n> <tspan style="font-size: 8.75px; " x="11.228816" y="0"> 2</t年代p一个n> <tspan style="font-size: 8.75px; " x="0" y="9.9399996"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="3.8508799" y="9.9399996"> =</t年代p一个n> <tspan style="font-size: 8.75px; " x="9.8459997" y="9.9399996"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,30.3,58.42)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="2.5006001" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,38.84,55.29)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,43.19,58.42)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n> </text> </g> </g> </svg>,<年代vg height="10.325" id="M124" style="vertical-align:-0.0pt;width:12.7px;" version="1.1" viewbox="0 0 12.7 10.325" width="12.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>是维数。CFLmax的数值结果<年代vg height="13.45" id="M125" style="vertical-align:-2.21957pt;width:45.775002px;" version="1.1" viewbox="0 0 45.775002 13.45" width="45.775002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 4</t年代p一个n> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="19.779745" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="32.345261" y="0"> )</t年代p一个n> </text> </g> </g> </svg>方案,FDTD(2, 2)表中列出<一个href="//www.newsama.com/journals/ijap/2012/956431/tab1/" target="_blank">1</一个>。相比之下,我们还画出色散曲线(4,4)和FDTD(2, 2)方法在图<一个href="//www.newsama.com/journals/ijap/2012/956431/fig3/" target="_blank">3</一个>。从图我们可以看出<一个href="//www.newsama.com/journals/ijap/2012/956431/fig3/" target="_blank">3</一个>,相对相位速度误差与采样点的增加/减少波长(PPW)。正如所料,(4,4)计划获得更好的数值色散FDTD(2, 2)方法。</p> <div class="floats-partial-section partial-other-wrapper" data-section="tab1"> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表1</年代p一个n> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijap/2012/956431/tab1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> CFLmax和准确性为不同的方法。</div> <a class="table-thumb-overlay" href="//www.newsama.com/journals/ijap/2012/956431/tab1" target="_blank" aria-label="View full page"></a> </div> </div> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-047d61808ce5015eceb7a5a5611dfb58"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2012/956431/figures/956431.fig.003.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-047d61808ce5015eceb7a5a5611dfb58 partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2012/956431/thumbnails/956431.fig.003_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-047d61808ce5015eceb7a5a5611dfb58 partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图3</年代p一个n> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijap/2012/956431/fig3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> <tbody> <tr> <td>数值色散曲线(4,4)方案和FDTD(2, 2)方法。</td> </tr> </tbody> </table> </div> </div> </div> </div> <h4 id="numerical-examples">4所示。数值例子</h4> <p>记住,我们不能选择的离散顺序<年代vg height="16.6625" id="M130" style="vertical-align:-4.74141pt;width:106.2375px;" version="1.1" viewbox="0 0 106.2375 16.6625" width="106.2375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6625)"> <g transform="translate(72,-58.67)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-65.56,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-60.38,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="9.364747" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="19.529686" y="0"> ∈</t年代p一个n> <tspan style="font-size: 12.50px; " x="31.570074" y="0"> {</t年代p一个n> <tspan style="font-size: 12.50px; " x="37.571514" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="44.448166" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="49.661915" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="55.863403" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="61.064651" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="67.30365" y="0"> }</t年代p一个n> </text> </g> </g> </svg>太大,因为这导致了大量的昂贵的部队在真实的应用程序中。在数值例子后,我们主要关注的演员<年代vg height="12.3" id="M131" style="vertical-align:-1.29163pt;width:43.037498px;" version="1.1" viewbox="0 0 43.037498 12.3" width="43.037498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.3)"> <g transform="translate(72,-62.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="16.028847" y="0"> ≤</t年代p一个n> <tspan style="font-size: 12.50px; " x="28.069235" y="0"> 4</t年代p一个n> </text> </g> </g> </svg>。</p> <h5 id="sec4.1">4.1。偶极子的辐射</h5> <p>我们认为是46的计算域由46个46细胞包围十点PML。一个垂直偶极子<我>P</我>是位于点(23)23日,23日,中心的域。测试的效率我们新的Pade近似应用在PML,人物<一个href="//www.newsama.com/journals/ijap/2012/956431/fig4/" target="_blank">4</一个>显示了<我>易之</我>场发射平面<年代vg height="10.9125" id="M132" style="vertical-align:-0.17555pt;width:43.612499px;" version="1.1" viewbox="0 0 43.612499 10.9125" width="43.612499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="10.239957" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="22.280346" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="28.531845" y="0"> 3</t年代p一个n> </text> </g> </g> </svg>89年之后的时间步骤。注意到的部分字段不是PML辐射同中心地从源,因为它应该。此外,垂直领域的结果<我>易之</我>点<年代vg height="13.45" id="M133" style="vertical-align:-2.21957pt;width:118.4875px;" version="1.1" viewbox="0 0 118.4875 13.45" width="118.4875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="16.666498" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="26.031246" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="32.282745" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="38.534245" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="47.911495" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="54.162994" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="63.202663" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="74.542885" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="80.794388" y="0"> /</t年代p一个n> <tspan style="font-size: 12.50px; " x="84.270218" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="90.521721" y="0"> )</t年代p一个n> </text> </g> </g> </svg>两个细胞,PML, FDTD(2, 2)和(4,4)计划总结在表<一个href="//www.newsama.com/journals/ijap/2012/956431/tab2/" target="_blank">2</一个>。注意,大致相同的计算成本,(4,4)方案使结果更准确比FDTD(2, 2)方法,进而被证明是一种很有前途的方法,精度高的优点,低计算资源和设施的大型模拟域和长时间。</p> <div class="floats-partial-section partial-other-wrapper" data-section="tab2"> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表2</年代p一个n> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijap/2012/956431/tab2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 比较的结果对FDTD(2, 2)和(4,4)计划。</div> <a class="table-thumb-overlay" href="//www.newsama.com/journals/ijap/2012/956431/tab2" target="_blank" aria-label="View full page"></a> </div> </div> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-4a82efa352c39f7ccbcecac030a7361c"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/ijap/volume-2012/956431/figures/956431.fig.004a.jpg"> <br> <strong>(一)</年代trong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/ijap/volume-2012/956431/figures/956431.fig.004b.jpg"> <br> <strong>(b)</年代trong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-4a82efa352c39f7ccbcecac030a7361c partial-carousel-thumbnail"> <button aria-label="Slide to (a) " class="partial-carousel-dot"><img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/ijap/volume-2012/956431/thumbnails/956431.fig.004a_th.jpg"><br><strong>(一)</年代trong></button> <button aria-label="Slide to (b) " class="partial-carousel-dot"><img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/ijap/volume-2012/956431/thumbnails/956431.fig.004b_th.jpg"><br><strong>(b)</年代trong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-4a82efa352c39f7ccbcecac030a7361c partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图4</年代p一个n> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijap/2012/956431/fig4/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> <tbody> <tr> <td>从偶极子辐射十点PML。(一)的分布<我>易之</我>字段。(b)的轮廓<我>易之</我>振幅。</td> </tr> </tbody> </table> </div> </div> </div> </div> <h5 id="sec4.2">4.2。散射介质的球体</h5> <p>接下来,考虑介质球被一个平面波的传播<我>z</我>方向和<我>E</我>极化的<我>x<b>- - - - - -</b></i>方向。入射波的频率为300 MHz。球体直径1.0米,相对介电常数<年代vg height="14.6" id="M134" style="vertical-align:-3.13504pt;width:51.700001px;" version="1.1" viewbox="0 0 51.700001 14.6" width="51.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-65.9,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-58.36,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 4</t年代p一个n> <tspan style="font-size: 12.50px; " x="18.291889" y="0"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="21.417639" y="0"> 0</t年代p一个n> </text> </g> </g> </svg>和电导率为零。我们使用统一的网格Δ<我>x =</我>Δ<我>y =</我>Δ<我>z =</我>Δ<我>。</我>总计算域是80到80年的80个细胞,总领域占据了32 32 32细胞,和ten-grid pml。我们表示相对雷达截面(RCS)的错误<年代p一个nclass="equation" id="EEq33"> <svg height="41.912498" id="M135" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 41.912498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,41.9125)"> <g transform="translate(72,-38.47)"> <text transform="matrix(1,0,0,-1,149.14,52.11)"> <tspan style="font-size: 12.50px; " x="43.34" y="-11.39"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="43.34" y="-8.2200003"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="0"> E</t年代p一个n> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> r</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.12791" y="0"> r</t年代p一个n> <tspan style="font-size: 12.50px; " x="16.228893" y="0"> o</t年代p一个n> <tspan style="font-size: 12.50px; " x="22.480394" y="0"> r</t年代p一个n> <tspan style="font-size: 12.50px; " x="30.094721" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="45.84" y="-9.8000002"> R</t年代p一个n> <tspan style="font-size: 12.50px; " x="53.854424" y="-9.8000002"> C</t年代p一个n> <tspan style="font-size: 12.50px; " x="62.193924" y="-9.8000002"> 年代</t年代p一个n> <tspan style="font-size: 12.50px; " x="71.921257" y="-9.8000002"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="83.261482" y="-9.8000002"> R</t年代p一个n> <tspan style="font-size: 12.50px; " x="91.288406" y="-9.8000002"> C</t年代p一个n> <tspan style="font-size: 12.50px; " x="99.627907" y="-9.8000002"> 年代</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,255.71,67.08)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,260.79,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="3.1700001"> |</t年代p一个n> </text> <g> <path d="m 192.48,55.23 70.81,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,211.19,43.89)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="3.1600001"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="2.5" y="1.58"> R</t年代p一个n> <tspan style="font-size: 12.50px; " x="10.526926" y="1.58"> C</t年代p一个n> <tspan style="font-size: 12.50px; " x="18.866426" y="1.58"> 年代</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,237,47.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,242.07,43.89)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="3.1600001"> |</t年代p一个n> <tspan style="font-size: 12.50px; " x="22.41" y="-8.2200003"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="225.8" y="-8.2200003"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="229.9635" y="-8.2200003"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="236.215" y="-8.2200003"> 8</t年代p一个n> <tspan style="font-size: 12.50px; " x="242.46649" y="-8.2200003"> )</t年代p一个n> </text> </g> </g> </svg></span>RCS *分析解决方案,RCS的解决方案与FDTD(2, 2),(4,2),或者(4,4)计划。图<一个href="//www.newsama.com/journals/ijap/2012/956431/fig5/" target="_blank">5</一个>显示RCS计算的相对误差与四阶精度在时域和四阶,分别在空间域二阶精度。</p> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-20c79d9dcb0f9f21a8604688d0a338f4"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/ijap/volume-2012/956431/figures/956431.fig.005a.jpg"> <br> <strong>(一)</年代trong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/ijap/volume-2012/956431/figures/956431.fig.005b.jpg"> <br> <strong>(b)</年代trong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-20c79d9dcb0f9f21a8604688d0a338f4 partial-carousel-thumbnail"> <button aria-label="Slide to (a) " class="partial-carousel-dot"><img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/ijap/volume-2012/956431/thumbnails/956431.fig.005a_th.jpg"><br><strong>(一)</年代trong></button> <button aria-label="Slide to (b) " class="partial-carousel-dot"><img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/ijap/volume-2012/956431/thumbnails/956431.fig.005b_th.jpg"><br><strong>(b)</年代trong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-20c79d9dcb0f9f21a8604688d0a338f4 partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图5</年代p一个n> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijap/2012/956431/fig5/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> <tbody> <tr> <td>RCS计算的相对误差与不同的方案在节能灯= 0.5。(一)<我>E</我>飞机(b)<我>H</我>飞机。</td> </tr> </tbody> </table> </div> </div> </div> </div> <p>我们可以看到,(4,4)计划更准确比(4,2)计划在同样的离散网格和CFL数。当网格也相应增大<年代vg height="10.9125" id="M136" style="vertical-align:-0.17555pt;width:50.337502px;" version="1.1" viewbox="0 0 50.337502 10.9125" width="50.337502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.490497" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="30.782387" y="0"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="33.908134" y="0"> 1</t年代p一个n> </text> </g> </g> </svg>,(4,2)计划的错误变得不可接受的。图<一个href="//www.newsama.com/journals/ijap/2012/956431/fig6/" target="_blank">6</一个>显示了比较(4,4)和(4,2)计划<年代vg height="11.0375" id="M137" style="vertical-align:-0.17555pt;width:67.712502px;" version="1.1" viewbox="0 0 67.712502 11.0375" width="67.712502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0375)"> <g transform="translate(72,-63.17)"> <text transform="matrix(1,0,0,-1,-71.95,63.4)"> <tspan style="font-size: 12.50px; " x="0" y="0"> C</t年代p一个n> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> F</t年代p一个n> <tspan style="font-size: 12.50px; " x="15.291169" y="0"> l</t年代p一个n> <tspan style="font-size: 12.50px; " x="26.393833" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="38.434223" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="44.685722" y="0"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="47.811474" y="0"> 6</t年代p一个n> </text> </g> </g> </svg>。在这种情况下,无论我们选择<年代vg height="11.1" id="M138" style="vertical-align:-0.17555pt;width:63.362499px;" version="1.1" viewbox="0 0 63.362499 11.1" width="63.362499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.1)"> <g transform="translate(72,-63.12)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.490497" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="30.782387" y="0"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="33.908134" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="40.159637" y="0"> 5</t年代p一个n> </text> </g> </g> </svg>或<年代vg height="10.9125" id="M139" style="vertical-align:-0.17555pt;width:50.337502px;" version="1.1" viewbox="0 0 50.337502 10.9125" width="50.337502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.490497" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="30.782387" y="0"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="33.908134" y="0"> 1</t年代p一个n> </text> </g> </g> </svg>计算结果(2,2)计划是不同的。原因可能是CFL数超过(2,2)方案的稳定性。(4,4)计划的结果仍可接受的除了在一些特定角度。图<一个href="//www.newsama.com/journals/ijap/2012/956431/fig7/" target="_blank">7</一个>显示了比较(4,4)和(2,2)方案与不同的离散网格和CFL数。很明显,高节能灯和粗网格数量,(4,4)计划的结果在某种程度上仍然是可以接受的。(2,2)方法中所花费的时间较长,约16分钟,大约12分钟(4,4)计划。的内存消耗大约30米(2,2)方法,和大约20米(4,4)计划。</p> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-6b2ea155f7a97a73c6b1aa24db9a1007"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2012/956431/figures/956431.fig.006.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-6b2ea155f7a97a73c6b1aa24db9a1007 partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2012/956431/thumbnails/956431.fig.006_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-6b2ea155f7a97a73c6b1aa24db9a1007 partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图6</年代p一个n> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijap/2012/956431/fig6/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> <tbody> <tr> <td>计算的相对误差<我>E</我>飞机的RCS与不同的方案在节能灯= 0.6。</td> </tr> </tbody> </table> </div> </div> </div> </div> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-a4a4805e49b3b3f5f34a9cfb339a947f"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2012/956431/figures/956431.fig.007.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-a4a4805e49b3b3f5f34a9cfb339a947f partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2012/956431/thumbnails/956431.fig.007_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-a4a4805e49b3b3f5f34a9cfb339a947f partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图7</年代p一个n> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijap/2012/956431/fig7/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> <tbody> <tr> <td>计算的相对误差<我>E</我>飞机的RCS(4, 4)和(2,2)计划。</td> </tr> </tbody> </table> </div> </div> </div> </div> <p>作为显示在图,我们可以得出一个结论如下。<年代p一个nclass="list"><span class="list-item"><span class="list-label">(我)</年代p一个n><span class="list-content">较小的空间离散网格我们解决,我们获得的数值精度高,不管我们采用什么方案。</年代p一个n></span><span class="list-item"><span class="list-label">(2)</年代p一个n><span class="list-content">具有相同空间discretizated计划,时间域的高阶离散,CFL数越高。</年代p一个n></span><span class="list-item"><span class="list-label">(3)</年代p一个n><span class="list-content">(4,4)计划与粗网格离散和高CFL数可以达到满意的数值结果,进而被证明是一种很有前途的方法,精度高的优点,低计算资源和设施的大领域和长期的模拟。</年代p一个n></span></span></p> <h4 id="conclusions">5。结论</h4> <p>我们提出优化算子分裂时变麦克斯韦方程组的数值解的方法在时域。总体介绍了高阶交错有限差分近似三维卷曲算子空间域。的效率<年代vg height="13.45" id="M140" style="vertical-align:-2.21957pt;width:45.775002px;" version="1.1" viewbox="0 0 45.775002 13.45" width="45.775002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 4</t年代p一个n> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="19.779745" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="32.345261" y="0"> )</t年代p一个n> </text> </g> </g> </svg>方案,特别是(4,4)方案,验证了一些数值例子。该方案的主要缺点是,它消耗的CPU时间超过了FDTD(2, 2)方法使用相同的网格大小。有效的并行算法是一个悬而未决的问题进行进一步的研究。</p> <h4 id="acknowledgments">确认</h4> <p>这项工作是支持的关键国家自然科学基金(没有。60931002)和大学安徽省自然科学基金(没有。KJ2011A002)。</p> </div> </div> <div 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fill="currentColor"></path> </svg></span><span>PDF</年代p一个n></span><span role="img" class="anticon ButtonGroup_buttonGroupWrapperIcon__CFikg"> <svg width="1em" height="1em" viewbox="0 0 20 22"> <defs> <clippath> <path fill-rule="evenodd" clip-rule="evenodd" d="M3,22a3,3,0,0,1-3-3V16a1,1,0,0,1,2,0v3a1,1,0,0,0,1,1H17a1,1,0,0,0,1-1V16a1,1,0,1,1,2,0v3a3,3,0,0,1-3,3Zm6.288-6.3-4-4a1,1,0,0,1,1.414-1.414L9,12.586V1a1,1,0,0,1,2,0V12.586l2.293-2.293a1,1,0,0,1,1.414,1.414l-4,4a1,1,0,0,1-1.423,0Z" fill="currentColor"></path> </clippath> </defs> <g> <path fill-rule="evenodd" clip-rule="evenodd" d="M3,22a3,3,0,0,1-3-3V16a1,1,0,0,1,2,0v3a1,1,0,0,0,1,1H17a1,1,0,0,0,1-1V16a1,1,0,1,1,2,0v3a3,3,0,0,1-3,3Zm6.288-6.3-4-4a1,1,0,0,1,1.414-1.414L9,12.586V1a1,1,0,0,1,2,0V12.586l2.293-2.293a1,1,0,0,1,1.414,1.414l-4,4a1,1,0,0,1-1.423,0Z" fill="currentColor"></path> </g> </svg></span></a> <a href="//www.newsama.com/journals/ijap/2012/956431.ris" class="ButtonGroup_buttonGroupWrapper__Rqhy0" role="button" type="ghost" aria-label="Download Citation" tabindex="0" unselectable="on" data-testid="download-citation"><span class="ButtonGroup_leftGroup__FJAmS"><span role="img" class="anticon ButtonGroup_buttonGroupWrapperIcon__CFikg"> <svg width="1em" height="1em" viewbox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"> <path d="M16 12H8C7.44772 12 7 12.4477 7 13C7 13.5523 7.44772 14 8 14H16C16.5523 14 17 13.5523 17 13C17 12.4477 16.5523 12 16 12Z" fill="currentColor"></path> <path d="M16 16H8C7.44772 16 7 16.4477 7 17C7 17.5523 7.44772 18 8 18H16C16.5523 18 17 17.5523 17 17C17 16.4477 16.5523 16 16 16Z" fill="currentColor"></path> <path d="M10 8H8C7.44772 8 7 8.44772 7 9C7 9.55228 7.44772 10 8 10H10C10.5523 10 11 9.55228 11 9C11 8.44772 10.5523 8 10 8Z" fill="currentColor"></path> <path d="M15 2C15 1.44772 14.5523 1 14 1C13.4477 1 13 1.44772 13 2V8C13 8.55228 13.4477 9 14 9H20C20.5523 9 21 8.55228 21 8C21 7.44772 20.5523 7 20 7H15V2Z" fill="currentColor"></path> <path fill-rule="evenodd" clip-rule="evenodd" d="M14.7071 1.29289C14.5196 1.10536 14.2652 1 14 1H6C4.34315 1 3 2.34315 3 4V20C3 21.6569 4.34315 23 6 23H18C19.6569 23 21 21.6569 21 20V8C21 7.73478 20.8946 7.48043 20.7071 7.29289L14.7071 1.29289ZM6 3H13.5858L19 8.41421V20C19 20.5523 18.5523 21 18 21H6C5.44772 21 5 20.5523 5 20V4C5 3.44772 5.44772 3 6 3Z" fill="currentColor"></path> </svg></span><span>下载引用</年代p一个n></span><span role="img" class="anticon ButtonGroup_buttonGroupWrapperIcon__CFikg"> <svg width="1em" height="1em" viewbox="0 0 20 22"> <defs> <clippath> <path fill-rule="evenodd" clip-rule="evenodd" d="M3,22a3,3,0,0,1-3-3V16a1,1,0,0,1,2,0v3a1,1,0,0,0,1,1H17a1,1,0,0,0,1-1V16a1,1,0,1,1,2,0v3a3,3,0,0,1-3,3Zm6.288-6.3-4-4a1,1,0,0,1,1.414-1.414L9,12.586V1a1,1,0,0,1,2,0V12.586l2.293-2.293a1,1,0,0,1,1.414,1.414l-4,4a1,1,0,0,1-1.423,0Z" fill="currentColor"></path> </clippath> </defs> <g> <path fill-rule="evenodd" clip-rule="evenodd" d="M3,22a3,3,0,0,1-3-3V16a1,1,0,0,1,2,0v3a1,1,0,0,0,1,1H17a1,1,0,0,0,1-1V16a1,1,0,1,1,2,0v3a3,3,0,0,1-3,3Zm6.288-6.3-4-4a1,1,0,0,1,1.414-1.414L9,12.586V1a1,1,0,0,1,2,0V12.586l2.293-2.293a1,1,0,0,1,1.414,1.414l-4,4a1,1,0,0,1-1.423,0Z" fill="currentColor"></path> </g> </svg></span></a> <div class="ant-collapse ant-collapse-icon-position-end articleToolbarOtherFormats_otherFormatsCollapse__VHaOL"> <div class="ant-collapse-item"> <div class="ant-collapse-header" aria-expanded="false" aria-disabled="false" role="button" tabindex="0"> <div class="ant-collapse-expand-icon"> <span role="img" class="anticon ant-collapse-arrow"> <svg width="1em" height="1em" viewbox="0 0 32 32" fill="none"> <path fill-rule="evenodd" clip-rule="evenodd" d="M17.773 23.453l11.2-11.265a1.918 1.918 0 000-2.641 1.75 1.75 0 00-2.542 0l-9.929 10.101-9.933-10.1a1.75 1.75 0 00-2.542 0 1.919 1.919 0 000 2.64L15.23 23.453c.352.365.811.547 1.271.547.46 0 .92-.182 1.271-.547z" fill="currentColor"></path> </svg></span> </div> <span class="ant-collapse-header-text"><span><span role="img" class="anticon articleToolbarOtherFormats_atofDownloadIcon__YRM5T"> <svg width="1em" height="1em" viewbox="0 0 20 22"> <defs> <clippath> <path fill-rule="evenodd" clip-rule="evenodd" d="M3,22a3,3,0,0,1-3-3V16a1,1,0,0,1,2,0v3a1,1,0,0,0,1,1H17a1,1,0,0,0,1-1V16a1,1,0,1,1,2,0v3a3,3,0,0,1-3,3Zm6.288-6.3-4-4a1,1,0,0,1,1.414-1.414L9,12.586V1a1,1,0,0,1,2,0V12.586l2.293-2.293a1,1,0,0,1,1.414,1.414l-4,4a1,1,0,0,1-1.423,0Z" fill="currentColor"></path> </clippath> </defs> <g> <path fill-rule="evenodd" clip-rule="evenodd" d="M3,22a3,3,0,0,1-3-3V16a1,1,0,0,1,2,0v3a1,1,0,0,0,1,1H17a1,1,0,0,0,1-1V16a1,1,0,1,1,2,0v3a3,3,0,0,1-3,3Zm6.288-6.3-4-4a1,1,0,0,1,1.414-1.414L9,12.586V1a1,1,0,0,1,2,0V12.586l2.293-2.293a1,1,0,0,1,1.414,1.414l-4,4a1,1,0,0,1-1.423,0Z" fill="currentColor"></path> </g> </svg></span><span>下载其他格式</年代p一个n></span></span> </div> </div> </div> <a href="//www.newsama.com/reprints/956431/confirm" class="ButtonGroup_buttonGroupWrapper__Rqhy0" role="button" type="ghost" aria-label="Order printed copies" tabindex="0" unselectable="on" target="_blank"><span class="ButtonGroup_leftGroup__FJAmS"><span role="img" class="anticon ButtonGroup_buttonGroupWrapperIcon__CFikg"> <svg width="1em" height="1em" viewbox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"> <path fill-rule="evenodd" clip-rule="evenodd" d="M7.41667 1H18.6667C19.1269 1 19.5 1.44772 19.5 2V22C19.5 22.5523 19.1269 23 18.6667 23H7.41667C5.80584 23 4.5 21.433 4.5 19.5V4.5C4.5 2.567 5.80584 1 7.41667 1ZM6.16667 16.3368V4.5C6.16667 3.67157 6.72631 3 7.41667 3H17.8333V16H7.41667C6.96933 16 6.54552 16.1208 6.16667 16.3368ZM17.8333 18H7.41667C6.72631 18 6.16667 18.6716 6.16667 19.5C6.16667 20.3284 6.72631 21 7.41667 21H17.8333V18Z" fill="currentColor"></path> </svg></span><span>订单打印副本</年代p一个n></span><span role="img" class="anticon ButtonGroup_buttonGroupWrapperIcon__CFikg"> <svg width="1em" height="1em" viewbox="0 0 18 14"> <defs> <clippath id="a"> <path d="M10.293,13.707a1,1,0,0,1,0-1.414L14.586,8H1A1,1,0,0,1,1,6H14.586L10.293,1.707A1,1,0,0,1,11.707.293l6,6a1,1,0,0,1,.172.231h0l.01.019,0,.005.007.014.006.012,0,.008.008.018v0a1,1,0,0,1-.009.817l0,0L17.9,7.44l0,.009-.005.011-.007.013,0,.008-.008.015,0,.005-.01.016,0,0-.011.017,0,0-.012.018,0,0-.012.017,0,0L17.8,7.6l0,0-.011.014,0,.006-.01.012-.009.011-.006.007-.015.017h0l-.04.042-6,6a1,1,0,0,1-1.414,0Z" transform="translate(3 5)"></path> </clippath> </defs> <g transform="translate(-3 -5)"> <path d="M10.293,13.707a1,1,0,0,1,0-1.414L14.586,8H1A1,1,0,0,1,1,6H14.586L10.293,1.707A1,1,0,0,1,11.707.293l6,6a1,1,0,0,1,.172.231h0l.01.019,0,.005.007.014.006.012,0,.008.008.018v0a1,1,0,0,1-.009.817l0,0L17.9,7.44l0,.009-.005.011-.007.013,0,.008-.008.015,0,.005-.01.016,0,0-.011.017,0,0-.012.018,0,0-.012.017,0,0L17.8,7.6l0,0-.011.014,0,.006-.01.012-.009.011-.006.007-.015.017h0l-.04.042-6,6a1,1,0,0,1-1.414,0Z" transform="translate(3 5)" fill="currentColor"></path> </g> </svg></span></a> <div class="articleToolbarStatistics_articleToolbarStatistics__8_woN"> <div class="articleToolbarStatistics_column__R2GqD"> <div> <div> <span>的观点</年代p一个n> <div class="articleToolbarStatistics_amount__vJIDp"> 992年</div> </div> <div> <span>下载</年代p一个n> <div class="articleToolbarStatistics_amount__vJIDp"> 1059年</div> </div> </div> </div> <div class="articleToolbarStatistics_column__R2GqD articleToolbarStatistics_dimensions__pe7pO"> <div> 引用</div> <span class="__dimensions_badge_embed__ articleToolbarStatistics_circle__p2dSc" data-doi="10.1155/2012/956431" data-style="small_circle"></span> </div> </div> <ul class="articleToolbarSocials_articleToolbarSocials__g02HH"> <li><a href="https://twitter.com/share?url=https://doi.org/10.1155/2012/956431&via=Hindawi" unselectable="on" title="" rel="noopener noreferrer" target="_blank"><span role="img" class="anticon"> <svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" viewbox="126.444 2.281 589 589"> <circle 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