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class="ArticleMiddleSection_articleMiddleSection__gAv9z"> <div class="articleHeader"> <div class="articleHeader__specialIssue"> <span class="articleHeader__specialIssue_tag">特殊的问题</年代pan> <h2 class="articleHeader__specialIssue_title">2011年分数微分方程</gydF4y2Bah2> <a href="//www.newsama.com/journals/ijde/si/565027/" class="articleHeader__specialIssue_url" target="_blank" rel="noreferrer">把这个特殊的问题</gydF4y2Baa> </div> <strong>研究文章|<!gydF4y2Ba-- -->开放获取</年代trong> <div class="articleHeader__meta"> <span>体积<!gydF4y2Ba-- -->2011年<!gydF4y2Ba-- -->|</年代pan> <span>文章的ID<!gydF4y2Ba-- -->231920年<!gydF4y2Ba-- -->|</年代pan> <span class="articleHeader__meta_doiLink"><a href="https://doi.org/10.1155/2011/231920" aria-label="Doi-link" target="_blank" rel="noreferrer">https://doi.org/10.1155/2011/231920</gydF4y2Baa></span> </div> <div class="simpleShowMore"> <button class="simpleShowMore__button">显示引用</gydF4y2Babutton> </div> <h1 class="articleHeader__title">一个显式的部分电缆方程的数值方法</gydF4y2Bah1> <div class="articleHeader__authors"> <span class="articleHeader__authors_author">j . Quintana-Murillo<年代up>1</年代up></span> <span class="articleHeader__authors_author">和<年代trong>s . b . Yuste</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 29.8-63.9l2.2-10.1v-837l-2.2-10.1c-7.1-31.8-21.9-58.3-44.6-80.1-20.2-19.2-43.9-31.7-73.6-38.5l-9.6-2.3L705 1.4c-321.9-.1-568.5.2-572.5.7zm1123.4 99.5c1.7.4 3.1 1 3.1 1.4 0 .5-125.6 87.7-279 194L700.9 490.2 422 297C268.5 190.7 143 103.4 143 103c0-.5 1-1.1 2.3-1.3 3.5-.7 1107.1-.8 1110.6-.1zM401 404c164.4 113.8 299.4 207 300 207 .6 0 135.6-93.2 300.1-207 164.5-113.9 299.3-207 299.5-207 .2 0 .4 170.9.4 379.7 0 417.9.5 386-6.1 398.3-6.2 11.6-19 21.4-31.9 24.4-5.8 1.4-67.4 1.6-562 1.6s-556.2-.2-562-1.6c-12.9-3-25.7-12.8-31.9-24.4-6.6-12.3-6.1 19.6-6.1-398.3 0-208.8.2-379.7.5-379.7S236.6 290.1 401 404z"></path> </svg></span></a><sup>1</年代up></span> </div> <div class="simpleShowMore"> <button class="simpleShowMore__button">显示更多</gydF4y2Babutton> </div> <div class="articleHeader__academicEditor"> <strong>学术编辑器:</年代trong> <span>Fawang刘</年代pan> </div> <div class="articleHeader__timeline"> <div class="articleHeader__timeline_item "> <strong>收到了</年代trong> <span>2011年4月27日</年代pan> </div> <div class="articleHeader__timeline_item "> <strong>接受</年代trong> <span>2011年6月30日</年代pan> </div> <div class="articleHeader__timeline_item articleHeader__timeline_item_sticky"> <strong>发表</年代trong> <span>2011年9月18日</年代pan> </div> </div> </div> <div class="articleBody"> <div class="xml-content"> <h4 class="header" id="abstract">文摘</gydF4y2Bah4> <p>显式数值方法解决部分电缆方程涉及两个时间Riemann-Liouville衍生品进行了研究。获得的数值差分近似的一阶导数的差分公式,Grunwald-Letnikov Riemann-Liouville衍生品的公式,为中心的三分的空间导数公式。方法的准确性、稳定性和收敛性。进行稳定性分析是通过一种冯诺依曼的方法适应分数方程。收敛性分析是一个类似的过程来完成。冯·诺依曼稳定性分析预测非常准确的条件目前的显式方法是稳定的。这是彻底的检查通过广泛的数字集成。</gydF4y2Bap> <span class="end-abs"></span> <h4 id="introduction">1。介绍</gydF4y2Bah4> <p>分数微积分是一个关键的工具,用于解决一些相关的科学问题在物理学、工程学、生物学、化学、水文等(<gydF4y2Baa href="#B1">1</gydF4y2Baa>- - - - - -<gydF4y2Baa href="#B6">6</gydF4y2Baa>]。的研究领域的分数形式主义尤为有用的反常扩散相关流程(<gydF4y2Baa href="#B1">1</gydF4y2Baa>,<gydF4y2Baa href="#B7">7</gydF4y2Baa>- - - - - -<gydF4y2Baa href="#B13">13</gydF4y2Baa>]。这种过程是非常丰富和重要的生物媒体(<gydF4y2Baa href="#B14">14</gydF4y2Baa>- - - - - -<gydF4y2Baa href="#B16">16</gydF4y2Baa>]。在这种背景下,离子神经元的电扩散是一个反常扩散问题的分数微积分最近被应用。的确切起源这一扩散过程的异常特征不明确(见[<gydF4y2Baa href="#B17">17</gydF4y2Baa>)和引用其中),但在任何情况下考虑的反常扩散的离子电扩散神经元的建模相关。最近这个问题已经解决Langlands et al。<gydF4y2Baa href="#B17">17</gydF4y2Baa>,<gydF4y2Baa href="#B18">18</gydF4y2Baa>]。一个方程,在他们的分析中扮演着重要角色下面的部分电缆(或电报员或均)方程(ⅱ型):<年代pan class="equation" id="EEq1"> <svg height="38.575001" id="M1" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 38.575001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,38.575)"> <g transform="translate(72,-41.14)"> <text transform="matrix(1,0,0,-1,121.01,60.7)"> <tspan style="font-size: 12.50px; 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" x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.3765302" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,218.11,47.77)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,224.18,46.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.16" y="-7.3299999"> −</t年代pan> <tspan style="font-size: 12.50px; " x="23.487719" y="-7.3299999"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,255.29,58.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,261.36,60.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,267.75,65.77)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,282.57,63.58)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,286.69,60.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 261.36,56.57 31.26,0" 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,-1,262.37,43.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,272.67,47.77)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,287.49,45.58)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,293.81,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="170.94" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="175.1035" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="181.355" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="184.48074" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="190.73225" y="0"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代pan class="equation" id="EEq2"> <svg height="40.1875" id="M2" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 40.1875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,40.1875)"> <g transform="translate(72,-39.85)"> <text transform="matrix(1,0,0,-1,103.74,60.21)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,110.13,65.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 101.79,56.09 15.24,0" 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,-1,101.79,44.21)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.3765302" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,112.09,48.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,118.23,52.96)"> <tspan style="font-size: 12.50px; " x="58.560001" y="-7.25"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.515023" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="14.678522" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="18.591961" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="26.231295" y="0"> ≡</t年代pan> </text> <g> <path d="m 157.7,56.09 44.44,0" 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,-1,157.7,44.21)"> <tspan style="font-size: 12.50px; " x="50.029999" y="-16"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</t年代pan> <tspan style="font-size: 12.50px; " x="9.4147587" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="13.578258" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="22.567915" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="33.908134" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="40.259659" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,215.13,65.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 204.53,56.09 18.65,0" 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,-1,204.53,44.21)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.3892732" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,218.33,47.65)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,226.46,45.26)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,233.46,66.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="-1.25" y="25.530001"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,239.17,52.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.6515961" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="30.83" y="-8.3500004"> </t年代pan> <tspan style="font-size: 12.50px; " x="41.345024" y="-8.3500004"> (</t年代pan> <tspan style="font-size: 12.50px; " x="45.508522" y="-8.3500004"> </t年代pan> <tspan style="font-size: 12.50px; " x="51.910057" y="-8.3500004"> )</t年代pan> </text> <g> <path d="m 253.42,56.09 58.42,0" 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,-1,253.42,42.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="22.192825" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="28.59436" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,286.18,47.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> +</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="14.808384" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="20.803505" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,313.04,52.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="151.71001" y="0.16"> (</t年代pan> <tspan style="font-size: 12.50px; " x="155.8735" y="0.16"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="162.125" y="0.16"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="165.25075" y="0.16"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="171.50224" y="0.16"> )</t年代pan> </text> </g> </g> </svg></span>与<年代vg height="13.6125" id="M3" style="vertical-align:-2.34499pt;width:87.837502px;" version="1.1" viewbox="0 0 87.837502 13.6125" width="87.837502" 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pan> <tspan style="font-size: 12.50px; " x="8.9896574" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="20.329878" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="30.057213" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="42.085098" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="51.912457" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="63.952847" y="0"> </t年代pan> </text> </g> </g> </svg>和<年代vg height="14.2" id="M4" style="vertical-align:-2.7337pt;width:70.449997px;" version="1.1" viewbox="0 0 70.449997 14.2" width="70.449997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2)"> <g transform="translate(72,-60.64)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.6773224" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="21.71771" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="25.193544" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="31.445045" y="0"> t</t年代pan> <tspan style="font-size: 12.50px; " x="34.920879" y="0"> e</t年代pan> <tspan style="font-size: 12.50px; " x="40.47221" y="0"> g</t年代pan> <tspan style="font-size: 12.50px; " x="46.548668" y="0"> e</t年代pan> <tspan style="font-size: 12.50px; " x="52.100002" y="0"> r</t年代pan> </text> </g> </g> </svg>是Riemann-Liouville分数导数。在这里<年代vg height="7.1624999" id="M5" style="vertical-align:-0.11285pt;width:7.5374999px;" version="1.1" viewbox="0 0 7.5374999 7.1624999" width="7.5374999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>之间的区别是膜电位和静止膜电位,<年代vg height="10.925" id="M6" style="vertical-align:-3.13504pt;width:14.1625px;" version="1.1" viewbox="0 0 14.1625 10.925" width="14.1625" 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pan> </text> <text transform="matrix(1,0,0,-1,-65.6,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg>是指数描述离子沿神经细胞的异常流量,然后呢<年代vg height="10.925" id="M7" style="vertical-align:-3.13504pt;width:14.1625px;" version="1.1" viewbox="0 0 14.1625 10.925" width="14.1625" 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pan> </text> <text transform="matrix(1,0,0,-1,-65.6,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>是指数描述跨膜的通量异常(<gydF4y2Baa href="#B17">17</gydF4y2Baa>,<gydF4y2Baa href="#B18">18</gydF4y2Baa>]。一些早期的部分电缆方程讨论了(<gydF4y2Baa href="#B19">19</gydF4y2Baa>,<gydF4y2Baa href="#B20">20.</gydF4y2Baa>]。</gydF4y2Bap> <p>各种分析和分式方程的数值方法来解决许多类已经提出和研究了在过去的几年里<gydF4y2Baa href="#B10">10</gydF4y2Baa>,<gydF4y2Baa href="#B21">21</gydF4y2Baa>- - - - - -<gydF4y2Baa href="#B30">30.</gydF4y2Baa>]。的数值方法,有限差分方法特别富有成果(<gydF4y2Baa href="#B31">31日</gydF4y2Baa>- - - - - -<gydF4y2Baa href="#B39">38</gydF4y2Baa>]。这些方法可以大致分为显式或隐式<gydF4y2Baa href="#B40">39</gydF4y2Baa>]。一个隐式方法来处理(<gydF4y2Baa href="#EEq1">1.1</gydF4y2Baa>)最近被刘et al。<gydF4y2Baa href="#B39">38</gydF4y2Baa>]。虽然隐式方法是更多的麻烦比显式方法,他们通常在更大的范围内保持稳定参数,尤其是对于大型的步伐,这使得它们特别适合部分扩散问题。然而,显式方法有一些特性,这些特性使其被广泛赞赏[<gydF4y2Baa href="#B32">32</gydF4y2Baa>,<gydF4y2Baa href="#B40">39</gydF4y2Baa>]:灵活性,简单起见,小的计算需求,简单概括空间维度高于1。不幸的是,他们可以在某些情况下变得不稳定,所以它是非常重要的,以确定这些方法的条件是稳定的。在本文中,我们将讨论一个显式有限差分格式求解部分电缆方程,这是接近的方法研究[<gydF4y2Baa href="#B32">32</gydF4y2Baa>,<gydF4y2Baa href="#B34">33</gydF4y2Baa>]。我们要解决两个主要问题:(i)这种方法能否应付部分涉及不同的分数阶导数的方程,如部分电缆方程;(2)是否冯诺依曼稳定性分析提出了(<gydF4y2Baa href="#B32">32</gydF4y2Baa>,<gydF4y2Baa href="#B35">34</gydF4y2Baa>适用于这类方程。</gydF4y2Bap> <h4 id="the-numerical-method">2。数值方法</gydF4y2Bah4> <p>从今以后,我们将使用符号<年代vg height="16.612499" id="M8" style="vertical-align:-4.77652pt;width:59.599998px;" version="1.1" viewbox="0 0 59.599998 16.612499" width="59.599998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6125)"> <g transform="translate(72,-58.71)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.07,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.17,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="16.891554" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="25.918718" y="0"> </t年代pan> </text> </g> </g> </svg>,<年代vg height="14.65" id="M9" style="vertical-align:-3.20526pt;width:60.0625px;" version="1.1" viewbox="0 0 60.0625 14.65" width="60.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.65)"> <g transform="translate(72,-60.28)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-68.04,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.85,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="20.905016" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="29.932182" y="0"> </t年代pan> </text> </g> </g> </svg>,<年代vg height="22.362499" id="M10" style="vertical-align:-5.84473pt;width:142.1375px;" version="1.1" viewbox="0 0 142.1375 22.362499" width="142.1375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,22.3625)"> <g transform="translate(72,-54.11)"> <text transform="matrix(1,0,0,-1,-71.95,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.9264221" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="10.089921" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-54.98,56.86)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-50.56,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-41.43,56.86)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-34.72,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-9.12,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,6.89,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≃</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,29.12,66.03)"> <tspan style="font-size: 8.75px; " x="-1.37" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> </g> </g> </svg>,在那里<年代vg height="22.362499" id="M11" style="vertical-align:-5.84473pt;width:28.5375px;" version="1.1" viewbox="0 0 28.5375 22.362499" width="28.5375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,22.3625)"> <g transform="translate(72,-54.11)"> <text transform="matrix(1,0,0,-1,-71.95,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-61.76,66.03)"> <tspan style="font-size: 8.75px; " x="-1.38" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> </g> </g> </svg>数值精确解的估计<年代vg height="13.45" id="M12" style="vertical-align:-2.21957pt;width:37.9375px;" version="1.1" viewbox="0 0 37.9375 13.45" width="37.9375" 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pan> <tspan style="font-size: 12.50px; " x="5.9264221" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="10.089921" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="16.966572" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="22.167818" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="26.081259" y="0"> )</t年代pan> </text> </g> </g> </svg>在<年代vg height="12.975" id="M13" style="vertical-align:-4.77652pt;width:42.237499px;" version="1.1" viewbox="0 0 42.237499 12.975" width="42.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.975)"> <g transform="translate(72,-61.62)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.339981" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.380369" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-42.69,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>和<年代vg height="12.975" id="M14" style="vertical-align:-3.20526pt;width:37.6875px;" version="1.1" viewbox="0 0 37.6875 12.975" width="37.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.975)"> <g transform="translate(72,-61.62)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-48.61,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>。</gydF4y2Bap> <p>我们为了得到数值差分算法,离散化连续微分和积分微分算子如下。离散化的部分我们使用Grunwald-Letnikov Riemann-Liouville导数公式<年代pan class="equation" id="EEq3"> <svg height="34.962502" id="M15" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 34.962502" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,34.9625)"> <g transform="translate(72,-44.03)"> <text transform="matrix(1,0,0,-1,116.27,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,123.67,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </t年代pan> </text> <g> <path d="m 114.69,56.84 25.88,0" 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,-1,114.69,44.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.6515961" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,125.25,48.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,141.77,53.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0019197" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="12.165419" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.042068" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="24.243317" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="28.156755" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="35.796089" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="47.836479" y="0"> Δ</t年代pan> </text> <text transform="matrix(1,0,0,-1,198.64,59.85)"> <tspan style="font-size: 8.75px; " x="0" y="9.8999996"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,213.96,53.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0100002" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.86" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="20.73665" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="25.937899" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,243.82,50.59)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,250.53,51.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.6300001" y="-2.51"> +</t年代pan> <tspan style="font-size: 12.50px; " x="19.970221" y="-2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="31.447975" y="-2.51"> (</t年代pan> <tspan style="font-size: 12.50px; " x="35.611473" y="-2.51"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="44.638641" y="-2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="48.552078" y="-2.51"> )</t年代pan> <tspan style="font-size: 12.50px; " x="214.22" y="-3.6900001"> (</t年代pan> <tspan style="font-size: 12.50px; " x="218.3835" y="-3.6900001"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="224.63499" y="-3.6900001"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="227.76074" y="-3.6900001"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="234.01225" y="-3.6900001"> )</t年代pan> </text> </g> </g> </svg></span>与<年代pan class="equation" id="EEq4"> <svg height="90.337502" id="M16" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 90.337502" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,90.3375)"> <g transform="translate(72,0.27)"> <text transform="matrix(1,0,0,-1,121.09,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代pan> </text> <text transform="matrix(1,0,0,-1,130.12,54.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="8.3500004"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,135.55,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.53" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="16.379999" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,155.84,46.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,162.55,47.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.3299999" y="-2.51"> =</t年代pan> <tspan style="font-size: 12.50px; " x="32.790001" y="-9.7700005"> 1</t年代pan> </text> <g> <path d="m 185.11,52.8 26.7,0" 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,-1,185.11,40.88)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.104103" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,206.38,46.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="11.6" y="-19.559999"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,213.01,43.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,213.53,35.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.7435842" y="0"> =</t年代pan> <tspan style="font-size: 8.75px; " x="10.738704" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,229.16,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,237.68,55.72)"> <tspan style="font-size: 8.75px; " x="0" y="10.69"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="7.8417921" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,248.94,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.53" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="16.379999" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,269.23,46.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="6.2139201" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="12.20904" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,286.68,47.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.9400001" y="-2.51"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="-142.14999" y="38.490002"> </t年代pan> <tspan style="font-size: 12.50px; " x="178.07001" y="-2.3599999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="182.23351" y="-2.3599999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="188.485" y="-2.3599999"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="191.61075" y="-2.3599999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="197.86224" y="-2.3599999"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,153.04,14.72)"> <tspan style="font-size: 8.75px; " x="0" y="10.69"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="7.850544" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,167.78,8.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="4.9200001"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.4" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="28.427166" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="40.970001" y="-7.2600002"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="49.997166" y="-7.2600002"> +</t年代pan> <tspan style="font-size: 12.50px; " x="61.337387" y="-7.2600002"> </t年代pan> </text> <g> <path d="m 208.75,11.8 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,-1,219.07,-0.08)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="18.299999" y="-3.8299999"> </t年代pan> <tspan style="font-size: 12.50px; " x="27.98" y="-8.75"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,255.57,14.72)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="7.8417921" y="0"> )</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="10.76"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.7435842" y="10.76"> −</t年代pan> <tspan style="font-size: 8.75px; " x="10.738704" y="10.76"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,271.18,8.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="193.57001" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="197.73351" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="203.985" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="207.11075" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="213.36224" y="0"> )</t年代pan> </text> </g> </g> </svg></span>和<年代vg height="21.125" id="M18" style="vertical-align:-4.85281pt;width:52.049999px;" version="1.1" viewbox="0 0 52.049999 21.125" width="52.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,21.125)"> <g transform="translate(72,-55.1)"> <text transform="matrix(1,0,0,-1,-71.95,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-63.44,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="10.76"> 0</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="7.850544" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-48.7,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> </text> </g> </g> </svg>。这些系数来自母函数(<gydF4y2Baa href="#B46">40</gydF4y2Baa>]<年代pan class="equation" id="EEq6"> <svg height="48.262501" id="M19" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.262501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.2625)"> <g transform="translate(72,-33.39)"> <text transform="matrix(1,0,0,-1,155.16,49.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1700001" y="0.0099999998"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="13.197166" y="0.0099999998"> −</t年代pan> <tspan style="font-size: 12.50px; " x="24.537388" y="0.0099999998"> </t年代pan> <tspan style="font-size: 12.50px; " x="30.776384" y="0.0099999998"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,190.1,54.95)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,199.01,49.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> </text> <text transform="matrix(1,0,0,-1,215.07,65.71)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</t年代pan> </text> <text transform="matrix(1,0,0,-1,211.05,43.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,211.57,36.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.7435842" y="0"> =</t年代pan> <tspan style="font-size: 8.75px; " x="10.738704" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,227.2,49.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,235.72,55.82)"> <tspan style="font-size: 8.75px; " x="0" y="10.7"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="7.8417921" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,246.98,49.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,253.22,54.77)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,258.46,49.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="206.28999" y="0.2"> (</t年代pan> <tspan style="font-size: 12.50px; " x="210.45351" y="0.2"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="216.705" y="0.2"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="219.83075" y="0.2"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="226.08224" y="0.2"> )</t年代pan> </text> </g> </g> </svg></span>离散化整数衍生品我们使用标准的公式:我们采用三点为中心的二阶空间导数公式<年代pan class="equation" id="EEq7"> <svg height="34.487499" id="M20" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 34.487499" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,34.4875)"> <g transform="translate(72,-44.41)"> <text transform="matrix(1,0,0,-1,128.84,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,135.23,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <g> <path d="m 125.41,56.84 18.14,0" 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,-1,125.41,44.59)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.3765302" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,138.67,48.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,144.74,53.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0100002" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.86" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,165.48,50.59)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,169.91,53.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,179.03,50.59)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,185.74,51.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.3299999" y="-2.51"> =</t年代pan> <tspan style="font-size: 12.50px; " x="21.357885" y="-2.51"> Δ</t年代pan> </text> <text transform="matrix(1,0,0,-1,216.13,58.86)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="8.2700005"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,221.44,53.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,227.37,59.76)"> <tspan style="font-size: 8.75px; " x="0" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,242.69,53.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="20.742477" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="24.905975" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="33.933144" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="40.809792" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,287.67,58.89)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,464.75,55.08)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="13.540749" y="0"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> )</t年代pan> </text> </g> </g> </svg></span>与<年代pan class="equation" id="EEq8"> <svg height="43.4375" id="M21" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 43.4375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,43.4375)"> <g transform="translate(72,-37.25)"> <text transform="matrix(1,0,0,-1,84.09,50.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代pan> </text> <text transform="matrix(1,0,0,-1,93.11,55.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="8.2700005"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,98.42,50.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,104.35,56.41)"> <tspan style="font-size: 8.75px; " x="0" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,120.37,50.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="13.23" y="-10.77"> </t年代pan> <tspan style="font-size: 12.50px; " x="21.24" y="-8.2600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="27.09" y="-10.77"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,154.34,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.4045279" y="0"> +</t年代pan> <tspan style="font-size: 8.75px; " x="9.3996477" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,168.61,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,177.73,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,184.45,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="34.23" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="40.080002" y="-2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.6300001" y="-2.51"> −</t年代pan> <tspan style="font-size: 12.50px; " x="19.957718" y="-2.51"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="26.209217" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,231.41,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,235.84,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,244.96,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,251.67,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="27.99" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="33.84" y="-2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.6300001" y="-2.51"> +</t年代pan> <tspan style="font-size: 12.50px; " x="19.970221" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,292.38,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.4045279" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="9.3996477" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,306.66,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,315.78,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,322.49,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 133.6,53.48 194.74,0" 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,-1,216.42,39.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="20.067314" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,240.65,44.68)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,329.54,50.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="135.21001" y="-1.14"> (</t年代pan> <tspan style="font-size: 12.50px; " x="139.3735" y="-1.14"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="145.625" y="-1.14"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="148.75075" y="-1.14"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="155.00224" y="-1.14"> )</t年代pan> </text> </g> </g> </svg></span>和一阶时间导数我们使用远期衍生品<年代pan class="equation" id="EEq9"> <svg height="30.737499" id="M22" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 30.737499" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,30.7375)"> <g transform="translate(72,-47.41)"> <text transform="matrix(1,0,0,-1,132.73,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 130.77,59.47 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,-1,130.77,47.59)"> <tspan style="font-size: 12.50px; " x="11.5" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.51" y="-6.2399998"> </t年代pan> <tspan style="font-size: 12.50px; " x="25.360001" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,163.01,53.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,167.44,56.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,176.56,53.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,183.27,53.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.3299999" y="-2.52"> =</t年代pan> <tspan style="font-size: 12.50px; " x="21.357885" y="-2.52"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,210.92,53.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,214.16,56.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,220.09,61.35)"> <tspan style="font-size: 8.75px; " x="0" y="9.0500002"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="6.2139201" y="0"> +</t年代pan> <tspan style="font-size: 8.75px; " x="12.20904" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,239.95,56.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="22.817974" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="26.981474" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="36.00864" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="39.922077" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="44.099998" y="-0.23"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="224.8" y="-0.23"> (</t年代pan> <tspan style="font-size: 12.50px; " x="228.9635" y="-0.23"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="235.215" y="-0.23"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="238.34074" y="-0.23"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="244.59225" y="-0.23"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代pan class="equation" id="EEq10"> <svg height="38.200001" id="M23" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 38.200001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,38.2)"> <g transform="translate(72,-41.44)"> <text transform="matrix(1,0,0,-1,122.49,50.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,128.78,47.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,132.02,50.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,137.95,55.36)"> <tspan style="font-size: 8.75px; " x="0" y="9.0500002"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="6.2139201" y="0"> +</t年代pan> <tspan style="font-size: 8.75px; " x="12.20904" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,158.5,50.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="13.24" y="-10.77"> </t年代pan> <tspan style="font-size: 12.50px; " x="21.25" y="-8.2600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="27.1" y="-10.77"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,192.48,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,196.9,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,206.03,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="6.2139201" y="0"> +</t年代pan> <tspan style="font-size: 8.75px; " x="12.20904" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,223.11,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="27.98" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="33.830002" y="-2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.6300001" y="-2.51"> −</t年代pan> <tspan style="font-size: 12.50px; " x="19.970221" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,263.82,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,268.25,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,277.37,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,284.08,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 171.74,53.48 118.2,0" 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,-1,224.37,41.61)"> <tspan style="font-size: 12.50px; " x="66.760002" y="-8.75"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="240.38" y="-11.99"> (</t年代pan> <tspan style="font-size: 12.50px; " x="244.5435" y="-11.99"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="250.795" y="-11.99"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="253.92075" y="-11.99"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="260.17224" y="-11.99"> )</t年代pan> </text> </g> </g> </svg></span>插入(<gydF4y2Baa href="#EEq3">2。1</gydF4y2Baa>),(<gydF4y2Baa href="#EEq7">2。5</gydF4y2Baa>)和(<gydF4y2Baa href="#EEq9">2。7</gydF4y2Baa>)(<gydF4y2Baa href="#EEq1">1.1</gydF4y2Baa>),一个人<年代pan class="equation" id="EEq11"> <svg height="28.9625" id="M24" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 28.9625" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,28.9625)"> <g transform="translate(72,-48.83)"> <text transform="matrix(1,0,0,-1,74.47,57.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,80.76,54.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,84,57.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,89.93,63.34)"> <tspan style="font-size: 8.75px; " x="0" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> +</t年代pan> <tspan style="font-size: 8.75px; " x="15.123456" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="19.499456" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,115.62,57.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="21.855244" y="0"> Δ</t年代pan> </text> <text transform="matrix(1,0,0,-1,146.51,63.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,161.33,61.79)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,146.51,53.53)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,167.54,52.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.3600001" y="-4.9200001"> Δ</t年代pan> </text> <text transform="matrix(1,0,0,-1,183.93,62.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="8.2799997"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,189.24,57.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,195.17,63.34)"> <tspan style="font-size: 8.75px; " x="0" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,207.71,52.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.38" y="-4.9200001"> +</t年代pan> <tspan style="font-size: 12.50px; " x="21.720221" y="-4.9200001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,237.05,62.29)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,241.92,57.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代pan> </text> <text transform="matrix(1,0,0,-1,250.95,63.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,265.77,61.79)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,250.95,53.53)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,269.89,57.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,275.81,63.34)"> <tspan style="font-size: 8.75px; " x="0" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,291.83,57.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="27.156515" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="34.033165" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="39.234413" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="43.147854" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="47.311352" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="172.92" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="177.0835" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="183.33499" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="186.46075" y="0"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="192.71225" y="0"> )</t年代pan> </text> </g> </g> </svg></span>在那里,可以很容易地证明,删除错误呢<年代vg height="13.45" id="M25" style="vertical-align:-2.21957pt;width:39.125px;" version="1.1" viewbox="0 0 39.125 13.45" width="39.125" 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pan> <tspan style="font-size: 12.50px; " x="6.8766499" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.040149" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.9168" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="23.118048" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="27.031487" y="0"> )</t年代pan> </text> </g> </g> </svg>是<年代pan class="equation" id="EEq12"> <svg height="18.674999" id="M26" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 18.674999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.675)"> <g transform="translate(72,-57.06)"> <text transform="matrix(1,0,0,-1,138.72,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.952628" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="15.116127" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="21.992777" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="27.206528" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="31.119967" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="38.7593" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="50.79969" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="62.277443" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="66.440941" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="75.468109" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="79.381546" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="86.320709" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="97.673439" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="107.07569" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="111.23919" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="120.26636" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="127.14301" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,270.03,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,274.9,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="183.59" y="-0.54000002"> (</t年代pan> <tspan style="font-size: 12.50px; " x="187.75349" y="-0.54000002"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="194.005" y="-0.54000002"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="197.13075" y="-0.54000002"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="203.38225" y="-0.54000002"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="209.63374" y="-0.54000002"> )</t年代pan> </text> </g> </g> </svg></span>忽视删除错误我们得到我们正在寻求的有限差分格式:<年代pan class="equation" id="EEq13"> <svg height="23.1625" id="M27" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 23.1625" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,23.1625)"> <g transform="translate(72,-53.47)"> <text transform="matrix(1,0,0,-1,89.04,59.34)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,95.33,56.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,98.56,59.34)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,108.75,65.39)"> <tspan style="font-size: 8.75px; " x="-1.37" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> +</t年代pan> <tspan style="font-size: 8.75px; " x="15.123456" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="19.499456" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,134.44,59.34)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="21.867746" y="0"> Δ</t年代pan> </text> <text transform="matrix(1,0,0,-1,165.34,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,180.16,63.85)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,165.34,55.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,188.45,59.34)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代pan> </text> <text transform="matrix(1,0,0,-1,197.48,64.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="8.2700005"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,202.79,59.34)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,212.98,65.39)"> <tspan style="font-size: 8.75px; " x="-1.38" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,228.3,59.34)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,247.25,64.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,252.13,59.34)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代pan> </text> <text transform="matrix(1,0,0,-1,261.16,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,275.97,63.85)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,261.16,55.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,280.1,59.34)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,290.29,65.39)"> <tspan style="font-size: 8.75px; " x="-1.38" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,306.3,59.34)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="152.19" y="-0.27000001"> (</t年代pan> <tspan style="font-size: 12.50px; " x="156.3535" y="-0.27000001"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="162.605" y="-0.27000001"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="165.73074" y="-0.27000001"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="171.98225" y="-0.27000001"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="178.23375" y="-0.27000001"> )</t年代pan> </text> </g> </g> </svg></span>也就是说,<年代pan class="equation" id="EEq14"> <svg height="48.387501" id="M28" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.387501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.3875)"> <g transform="translate(72,-33.29)"> <text transform="matrix(1,0,0,-1,-4.96,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,5.23,55.72)"> <tspan style="font-size: 8.75px; " x="-1.38" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> +</t年代pan> <tspan style="font-size: 8.75px; " x="15.123456" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="19.499456" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,31.61,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,53.84,55.72)"> <tspan style="font-size: 8.75px; " x="-1.38" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,69.16,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,94.47,65.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,89.5,43.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,90.02,35.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.7435842" y="0"> =</t年代pan> <tspan style="font-size: 8.75px; " x="10.738704" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,105.66,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,114.17,56.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,128.99,54.17)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,114.17,45.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,135.2,44.75)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.3600001" y="-4.9200001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,152.75,55.72)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="15.123456" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="19.867041" y="0"> )</t年代pan> <tspan style="font-size: 8.75px; " x="-1.38" y="10.76"> </t年代pan> <tspan style="font-size: 8.75px; " x="2.024528" y="10.76"> +</t年代pan> <tspan style="font-size: 8.75px; " x="8.0196476" y="10.76"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,178.81,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="17.591721" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,206.59,55.72)"> <tspan style="font-size: 8.75px; " x="-1.37" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="15.123456" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="19.867041" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,232.65,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,254.18,55.72)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="15.123456" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="19.867041" y="0"> )</t年代pan> <tspan style="font-size: 8.75px; " x="-1.37" y="10.76"> </t年代pan> <tspan style="font-size: 8.75px; " x="2.034528" y="10.76"> −</t年代pan> <tspan style="font-size: 8.75px; " x="8.0296478" y="10.76"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,277.46,44.75)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.38" y="-4.9200001"> −</t年代pan> <tspan style="font-size: 12.50px; " x="21.720221" y="-4.9200001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,306.8,54.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,311.68,49.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.104103" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,332.94,54.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,337.39,52.66)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,346.48,65.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,341.51,43.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,342.03,35.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.7435842" y="0"> =</t年代pan> <tspan style="font-size: 8.75px; " x="10.738704" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,357.67,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,366.18,56.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,381,54.17)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,366.18,45.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,385.12,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,395.31,55.72)"> <tspan style="font-size: 8.75px; " x="-1.38" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="15.123456" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="19.867041" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,418.59,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="39.900002" y="0.15000001"> (</t年代pan> <tspan style="font-size: 12.50px; " x="44.063499" y="0.15000001"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="50.314999" y="0.15000001"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="53.44075" y="0.15000001"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="59.692249" y="0.15000001"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="65.943748" y="0.15000001"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代pan class="equation" id="EEq15"> <svg height="38.025002" id="M29" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 38.025002" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,38.025)"> <g transform="translate(72,-41.58)"> <text transform="matrix(1,0,0,-1,173.62,54.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.590281" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="23.630671" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="35.360001" y="-8.2299995"> (</t年代pan> <tspan style="font-size: 12.50px; " x="39.523499" y="-8.2299995"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="48.550667" y="-8.2299995"> </t年代pan> <tspan style="font-size: 12.50px; " x="52.464104" y="-8.2299995"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,230.25,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,234.69,65.9)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代pan> </text> <g> <path d="m 208.98,57.82 29.83,0" 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,-1,209.34,43.84)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="20.067314" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,233.57,49.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,240.01,54.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="218.48" y="1.02"> (</t年代pan> <tspan style="font-size: 12.50px; " x="222.64349" y="1.02"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="228.895" y="1.02"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="232.02075" y="1.02"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="238.27225" y="1.02"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="244.52374" y="1.02"> )</t年代pan> </text> </g> </g> </svg></span></p> <p>为了测试该算法,我们解决了(<gydF4y2Baa href="#EEq1">1.1</gydF4y2Baa>)的时间间隔<年代vg height="12.3" id="M30" style="vertical-align:-1.29163pt;width:104.65px;" version="1.1" viewbox="0 0 104.65 12.3" width="104.65" 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pan> <tspan style="font-size: 12.50px; " x="8.5645552" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.416679" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="20.892513" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="30.607344" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="42.647732" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="53.000217" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="65.040604" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="73.892731" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="77.368561" y="0"> 2</t年代pan> </text> </g> </g> </svg>吸收边界条件,<年代vg height="13.45" id="M31" style="vertical-align:-2.21957pt;width:218.28751px;" version="1.1" viewbox="0 0 218.28751 13.45" width="218.28751" 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pan> <tspan style="font-size: 12.50px; " x="5.9264221" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="10.089921" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="20.429901" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="32.470291" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="41.034847" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="49.886971" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="53.362804" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="59.614304" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="64.828056" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="68.741493" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="76.368324" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="88.408714" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="94.335136" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="98.498634" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="108.85112" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="120.89151" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="129.74364" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="133.21947" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="139.47096" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="144.67221" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="148.58565" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="156.22499" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="168.26538" y="0"> 0</t年代pan> </text> </g> </g> </svg>,初始条件由狄拉克δ函数集中的<年代vg height="10.9125" id="M32" style="vertical-align:-0.17555pt;width:35.924999px;" version="1.1" viewbox="0 0 35.924999 10.9125" width="35.924999" 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pan> <tspan style="font-size: 12.50px; " x="10.339981" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.380369" y="0"> 0</t年代pan> </text> </g> </g> </svg>:<年代vg height="13.45" id="M33" style="vertical-align:-2.21957pt;width:87.112503px;" version="1.1" viewbox="0 0 87.112503 13.45" width="87.112503" 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pan> <tspan style="font-size: 12.50px; " x="5.9264221" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="10.089921" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="16.966572" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="22.167818" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="28.419319" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="36.058651" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="48.099041" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="54.38805" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="58.551548" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="65.4282" y="0"> )</t年代pan> </text> </g> </g> </svg>。这个问题的精确解<年代vg height="10.325" id="M34" style="vertical-align:-0.0pt;width:54.025002px;" version="1.1" viewbox="0 0 54.025002 10.325" width="54.025002" 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pan> <tspan style="font-size: 12.50px; " x="14.403456" y="0"> →</t年代pan> <tspan style="font-size: 12.50px; " x="31.532566" y="0"> ∞</t年代pan> </text> </g> </g> </svg>是(<gydF4y2Baa href="#B17">17</gydF4y2Baa>]<年代pan class="equation" id="EEq16"> <svg height="70.737503" id="M35" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 70.737503" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,70.7375)"> <g transform="translate(72,-15.41)"> <text transform="matrix(1,0,0,-1,44.61,40.58)"> <tspan style="font-size: 12.50px; " x="64.879997" y="-7.25"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0019197" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="12.165419" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.042068" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="24.243317" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="28.156755" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="35.796089" y="0"> =</t年代pan> </text> <g> <path d="m 93.65,43.71 37.94,0" 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,-1,93.65,27.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> √</t年代pan> </text> <g> <path d="m 105.25,39.58 26.34,0" 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,-1,105.25,27.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,115.42,31.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,119.86,28.84)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,123.99,27.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,136.81,56.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</t年代pan> </text> <text transform="matrix(1,0,0,-1,132.78,34.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,133.3,26.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.7435842" y="0"> =</t年代pan> <tspan style="font-size: 8.75px; " x="10.738704" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,150.13,48.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.52"> −</t年代pan> <tspan style="font-size: 12.50px; " x="14.414555" y="-2.52"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,172.16,56.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,177.04,51.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,180.95,56.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,185.4,53.97)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,189.52,48.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,195.37,58.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 150.13,43.71 50.48,0" 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,-1,169.9,31.83)"> <tspan style="font-size: 12.50px; " x="31.91" y="-8.75"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.7766261" y="0"> !</t年代pan> </text> <text transform="matrix(1,0,0,-1,213.85,46.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ,</t年代pan> <tspan style="font-size: 8.75px; " x="6.5640001" y="0"> 0</t年代pan> <tspan style="font-size: 8.75px; " x="-1.13" y="10.46"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="3.2460001" y="10.46"> ,</t年代pan> <tspan style="font-size: 8.75px; " x="5.434" y="10.46"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,227.37,56.89)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⎡</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="9.75"> ⎢</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="19.5"> ⎢</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="29.25"> ⎢</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="38.939999"> ⎣</t年代pan> <tspan style="font-size: 12.50px; " x="10.31" y="9.0600004"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,244.56,52.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <g> <path d="m 234.19,43.71 18.73,0" 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,-1,234.19,31.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,244.36,35.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,248.8,33.45)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,256.2,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="10.67"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="21.33"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="32"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="42.66"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="45.830002"> |</t年代pan> <tspan style="font-size: 12.50px; " x="5.4899998" y="11.46"> </t年代pan> <tspan style="font-size: 12.50px; " x="34.43" y="-2.5899999"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.86" y="6.54"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="21.887165" y="6.54"> −</t年代pan> </text> <text transform="matrix(1,0,0,-1,296.98,62.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <g> <path d="m 290.63,60.08 11.22,0" 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,-1,293.11,48.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="12.72" y="-8.7600002"> +</t年代pan> <tspan style="font-size: 12.50px; " x="24.047718" y="-8.7600002"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,323.52,53.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,328.4,56.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.7766261" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="11.977874" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,346.73,53.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,351.61,52.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="-52.48" y="31.42"> </t年代pan> <tspan style="font-size: 12.50px; " x="-43.919998" y="19.24"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="-85.809998" y="26.49"> (</t年代pan> <tspan style="font-size: 12.50px; " x="-81.6465" y="26.49"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="-75.395004" y="26.49"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="-70.193756" y="26.49"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="-63.942253" y="26.49"> )</t年代pan> <tspan style="font-size: 12.50px; " x="-57.690754" y="26.49"> ,</t年代pan> </text> <g> <path d="m 307.69,28.67 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,-1,307.69,16.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="39.810001" y="-3.8299999"> </t年代pan> <tspan style="font-size: 12.50px; " x="55.700001" y="-40.099998"> ⎤</t年代pan> <tspan style="font-size: 12.50px; " x="55.700001" y="-30.35"> ⎥</t年代pan> <tspan style="font-size: 12.50px; " x="55.700001" y="-20.6"> ⎥</t年代pan> <tspan style="font-size: 12.50px; " x="55.700001" y="-10.85"> ⎥</t年代pan> <tspan style="font-size: 12.50px; " x="55.700001" y="-1.16"> ⎦</t年代pan> <tspan style="font-size: 12.50px; " x="10.23" y="-8.75"> +</t年代pan> <tspan style="font-size: 12.50px; " x="21.570221" y="-8.75"> </t年代pan> <tspan style="font-size: 12.50px; " x="28.346848" y="-8.75"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="33.548096" y="-8.75"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="61.330002" y="-23.790001"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="150.8" y="-23.790001"> (</t年代pan> <tspan style="font-size: 12.50px; " x="154.9635" y="-23.790001"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="161.215" y="-23.790001"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="164.34074" y="-23.790001"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="170.59225" y="-23.790001"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="176.84375" y="-23.790001"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="10.325" id="M36" style="vertical-align:-0.0pt;width:15.175px;" version="1.1" viewbox="0 0 15.175 10.325" width="15.175" 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pan> </text> </g> </g> </svg>狐狸表示<年代vg height="10.325" id="M37" style="vertical-align:-0.0pt;width:15.175px;" version="1.1" viewbox="0 0 15.175 10.325" width="15.175" 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pan> </text> </g> </g> </svg>函数(<gydF4y2Baa href="#B10">10</gydF4y2Baa>,<gydF4y2Baa href="#B47">41</gydF4y2Baa>]。在我们的数值程序,准确的初始条件<年代vg height="13.45" id="M38" style="vertical-align:-2.21957pt;width:87.112503px;" version="1.1" viewbox="0 0 87.112503 13.45" width="87.112503" 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pan> <tspan style="font-size: 12.50px; " x="5.9264221" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="10.089921" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="16.966572" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="22.167818" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="28.419319" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="36.058651" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="48.099041" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="54.38805" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="58.551548" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="65.4282" y="0"> )</t年代pan> </text> </g> </g> </svg>是近似的<年代pan class="equation" id="EEq17"> <svg height="59.075001" id="M39" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 59.075001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,59.075)"> <g transform="translate(72,-24.74)"> <text transform="matrix(1,0,0,-1,142.94,45.24)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0100002" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.87" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,163.68,42.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,168.11,45.24)"> <tspan style="font-size: 12.50px; " x="11.46" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="20.790001" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="32.82" y="-12.07"> ⎧</t年代pan> <tspan style="font-size: 12.50px; " x="32.82" y="-6.9400001"> ⎪</t年代pan> <tspan style="font-size: 12.50px; " x="32.82" y="3.1900001"> ⎨</t年代pan> <tspan style="font-size: 12.50px; " x="32.82" y="13.31"> ⎪</t年代pan> <tspan style="font-size: 12.50px; " x="32.82" y="18.379999"> ⎩</t年代pan> <tspan style="font-size: 12.50px; " x="46.849998" y="-18.26"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> 0</t年代pan> </text> <g> <path d="m 210.13,59.37 15.91,0" 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,-1,210.13,47.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.1" y="-8.7600002"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="32.728748" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="41.055748" y="-8.7600002"> =</t年代pan> <tspan style="font-size: 12.50px; " x="53.096138" y="-8.7600002"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="59.347637" y="-8.7600002"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="-1.1900001" y="18.200001"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="5.0615001" y="18.200001"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="32.718136" y="18.200001"> </t年代pan> <tspan style="font-size: 12.50px; " x="40.419983" y="18.200001"> ≠</t年代pan> <tspan style="font-size: 12.50px; " x="51.07254" y="18.200001"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="57.324039" y="18.200001"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="248.36" y="2.25"> (</t年代pan> <tspan style="font-size: 12.50px; " x="252.5235" y="2.25"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="258.77499" y="2.25"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="261.90076" y="2.25"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="268.15225" y="2.25"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="274.40375" y="2.25"> )</t年代pan> </text> </g> </g> </svg></span>显式差分格式(<gydF4y2Baa href="#EEq14">2.12</gydF4y2Baa>)是测试通过对比解析解与数值解后的几个案例描述的问题(<gydF4y2Baa href="#EEq15">2.13</gydF4y2Baa>)和不同的价值观<年代vg height="10.925" id="M40" style="vertical-align:-3.13504pt;width:14.1625px;" version="1.1" viewbox="0 0 14.1625 10.925" width="14.1625" 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pan> </text> <text transform="matrix(1,0,0,-1,-65.6,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg>和<年代vg height="10.925" id="M41" style="vertical-align:-3.13504pt;width:14.1625px;" version="1.1" viewbox="0 0 14.1625 10.925" width="14.1625" 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pan> </text> <text transform="matrix(1,0,0,-1,-65.6,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>。我们计算了解析解的(<gydF4y2Baa href="#EEq16">2.14</gydF4y2Baa>)删除系列<年代vg height="10.9125" id="M42" 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pan> <tspan style="font-size: 12.50px; " x="10.239957" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.280346" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="28.531845" y="0"> 0</t年代pan> </text> </g> </g> </svg>。相应的狐狸<年代vg height="10.325" id="M43" style="vertical-align:-0.0pt;width:15.175px;" version="1.1" viewbox="0 0 15.175 10.325" width="15.175" 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pan> </text> </g> </g> </svg>描述的功能是评估通过级数展开(<gydF4y2Baa href="#B10">10</gydF4y2Baa>,<gydF4y2Baa href="#B47">41</gydF4y2Baa>]删除后的无穷级数前50。在数据<gydF4y2Baa href="//www.newsama.com/journals/ijde/2011/231920/fig1/" target="_blank">1</gydF4y2Baa>和<gydF4y2Baa href="//www.newsama.com/journals/ijde/2011/231920/fig2/" target="_blank">2</gydF4y2Baa>我们展示的两个值的分析和数值解<年代vg height="10.925" id="M44" style="vertical-align:-3.13504pt;width:14.1625px;" version="1.1" viewbox="0 0 14.1625 10.925" width="14.1625" 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pan> </text> <text transform="matrix(1,0,0,-1,-65.6,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg>和<年代vg height="10.925" id="M45" style="vertical-align:-3.13504pt;width:14.1625px;" version="1.1" viewbox="0 0 14.1625 10.925" width="14.1625" 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pan> </text> <text transform="matrix(1,0,0,-1,-65.6,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>在<年代vg height="10.9125" id="M46" style="vertical-align:-0.17555pt;width:35.924999px;" version="1.1" viewbox="0 0 35.924999 10.9125" width="35.924999" 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pan> <tspan style="font-size: 12.50px; " x="10.339981" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.380369" y="0"> 0</t年代pan> </text> </g> </g> </svg>和<年代vg height="11.1" id="M47" style="vertical-align:-0.17555pt;width:47.650002px;" version="1.1" viewbox="0 0 47.650002 11.1" width="47.650002" 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pan> <tspan style="font-size: 12.50px; " x="10.339981" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.380369" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="28.63187" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="31.75762" y="0"> 5</t年代pan> </text> </g> </g> </svg>。准确和数值解之间的差异数据所示<gydF4y2Baa href="//www.newsama.com/journals/ijde/2011/231920/fig3/" target="_blank">3</gydF4y2Baa>和<gydF4y2Baa href="//www.newsama.com/journals/ijde/2011/231920/fig4/" target="_blank">4</gydF4y2Baa>。一看到,除了很短的时间,该协议相当好。的大值误差小次部分是由于狄拉克δ函数的近似<年代vg height="10.9125" id="M48" style="vertical-align:-0.17555pt;width:35.924999px;" version="1.1" viewbox="0 0 35.924999 10.9125" width="35.924999" 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pan> <tspan style="font-size: 12.50px; " x="10.339981" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.380369" y="0"> 0</t年代pan> </text> </g> </g> </svg>由(<gydF4y2Baa href="#EEq17">2.15</gydF4y2Baa>)。这显然是赞赏,当注意到不同尺度的数据<gydF4y2Baa href="//www.newsama.com/journals/ijde/2011/231920/fig3/" target="_blank">3</gydF4y2Baa>和<gydF4y2Baa href="//www.newsama.com/journals/ijde/2011/231920/fig4/" target="_blank">4</gydF4y2Baa>:误差要小得多<年代vg height="11.1" id="M49" style="vertical-align:-0.17555pt;width:47.650002px;" version="1.1" viewbox="0 0 47.650002 11.1" width="47.650002" 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pan> <tspan style="font-size: 12.50px; " x="10.339981" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.380369" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="28.63187" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="31.75762" y="0"> 5</t年代pan> </text> </g> </g> </svg>比<年代vg height="10.9125" id="M50" style="vertical-align:-0.17555pt;width:35.924999px;" version="1.1" viewbox="0 0 35.924999 10.9125" width="35.924999" 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pan> <tspan style="font-size: 12.50px; " x="10.339981" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.380369" y="0"> 0</t年代pan> </text> </g> </g> </svg>。为例<年代vg height="14.6" id="M51" style="vertical-align:-3.13504pt;width:53.525002px;" version="1.1" viewbox="0 0 53.525002 14.6" width="53.525002" 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pan> </text> <text transform="matrix(1,0,0,-1,-65.6,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.25,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="21.75522" y="0"> 2</t年代pan> </text> </g> </g> </svg>我们使用一个较小的值<年代vg height="10.8" id="M52" 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pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代pan> </text> </g> </g> </svg>同时,一个更大的价值<年代vg height="10.8" id="M53" style="vertical-align:-0.11285pt;width:20px;" version="1.1" viewbox="0 0 20 10.8" width="20" 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pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代pan> </text> </g> </g> </svg>比的情况下<年代vg height="14.6" id="M54" style="vertical-align:-3.13504pt;width:41.362499px;" version="1.1" viewbox="0 0 41.362499 14.6" width="41.362499" 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pan> </text> <text transform="matrix(1,0,0,-1,-65.6,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.25,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> </text> </g> </g> </svg>为了保持稳定的数值方案。节将讨论这个问题<gydF4y2Baa href="#sec3">3</gydF4y2Baa>。</gydF4y2Bap> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-135a254247cad356263b4e4d3efbd096"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijde/volume-2011/231920/figures/231920.fig.001.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-135a254247cad356263b4e4d3efbd096 partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijde/volume-2011/231920/thumbnails/231920.fig.001_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-135a254247cad356263b4e4d3efbd096 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pan> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijde/2011/231920/fig1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> <tbody> <tr> <td>在中点数值解<年代vg height="10.9125" id="M55" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 35.924999 10.9125" width="35.924999" 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pan> <tspan style="font-size: 12.50px; " x="10.339981" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.380369" y="0"> 0</t年代pan> </text> </g> </g> </svg>(空心符号)<年代vg height="11.1" id="M56" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 47.650002 11.1" width="47.650002" 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pan> <tspan style="font-size: 12.50px; " x="10.339981" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.380369" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="28.63187" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="31.75762" y="0"> 5</t年代pan> </text> </g> </g> </svg>(填充符号)的部分电缆方程<年代vg height="14.6" id="M57" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 41.362499 14.6" width="41.362499" 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pan> </text> <text transform="matrix(1,0,0,-1,-65.6,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.25,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.6" id="M58" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 41.362499 14.6" width="41.362499" 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pan> </text> <text transform="matrix(1,0,0,-1,-65.6,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.25,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> </text> </g> </g> </svg>(广场),<年代vg height="14.6" id="M59" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 53.525002 14.6" width="53.525002" 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pan> </text> <text transform="matrix(1,0,0,-1,-65.6,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.25,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="21.75522" y="0"> 2</t年代pan> </text> </g> </g> </svg>(圈)<年代vg height="10.9125" id="M60" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 67.175003 10.9125" width="67.175003" 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pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.367147" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="31.407536" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="37.659035" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="41.134869" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="47.386372" y="0"> 0</t年代pan> </text> </g> </g> </svg>,<年代vg height="14.2" id="M61" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 64.900002 14.2" width="64.900002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2)"> <g transform="translate(72,-60.64)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="16.403936" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="28.444324" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="34.695824" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-31,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 4</t年代pan> </text> </g> </g> </svg>,<年代vg height="13.55" id="M62" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 68.137497 13.55" width="68.137497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="36.121166" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="48.161556" y="0"> 1</t年代pan> </text> </g> </g> </svg>,<年代vg height="11.1" id="M63" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 38.387501 11.1" width="38.387501" 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pan> <tspan style="font-size: 12.50px; " x="12.315455" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="24.355844" y="0"> 5</t年代pan> </text> </g> </g> </svg>。线的精确解(<gydF4y2Baa href="https://static.hindawi.com/articles/ijde/volume-2011/231920/figures/231920/">2.14</gydF4y2Baa>)。</tgydF4y2Bad> </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-01cb4e905970789b9cb06d27f0902e6d"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijde/volume-2011/231920/figures/231920.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-01cb4e905970789b9cb06d27f0902e6d partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijde/volume-2011/231920/thumbnails/231920.fig.002_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-01cb4e905970789b9cb06d27f0902e6d 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pan> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijde/2011/231920/fig2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> <tbody> <tr> <td>在中点数值解<年代vg height="10.9125" id="M64" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 35.924999 10.9125" width="35.924999" 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pan> <tspan style="font-size: 12.50px; " x="10.339981" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.380369" y="0"> 0</t年代pan> </text> </g> </g> </svg>(空心符号)<年代vg height="11.1" id="M65" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 47.650002 11.1" width="47.650002" 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pan> <tspan style="font-size: 12.50px; " x="10.339981" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.380369" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="28.63187" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="31.75762" y="0"> 5</t年代pan> </text> </g> </g> </svg>(填充符号)的部分电缆方程<年代vg height="14.6" id="M66" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 53.525002 14.6" width="53.525002" 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pan> </text> <text transform="matrix(1,0,0,-1,-65.6,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.25,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="21.75522" y="0"> 2</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.6" id="M67" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 41.362499 14.6" width="41.362499" 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pan> </text> <text transform="matrix(1,0,0,-1,-65.6,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.25,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> </text> </g> </g> </svg>(广场),<年代vg height="14.6" id="M68" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 53.525002 14.6" width="53.525002" 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pan> </text> <text transform="matrix(1,0,0,-1,-65.6,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.25,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="21.75522" y="0"> 2</t年代pan> </text> </g> </g> </svg>(圈)<年代vg height="10.9125" id="M69" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 67.175003 10.9125" width="67.175003" 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pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.367147" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="31.407536" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="37.659035" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="41.134869" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="47.386372" y="0"> 0</t年代pan> </text> </g> </g> </svg>,<年代vg height="14.3375" id="M70" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 64.900002 14.3375" width="64.900002" 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,-71.95,60.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="16.403936" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="28.444324" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="34.695824" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-31,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 5</t年代pan> </text> </g> </g> </svg>,<年代vg height="13.55" id="M71" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 68.137497 13.55" width="68.137497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="36.121166" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="48.161556" y="0"> 1</t年代pan> </text> </g> </g> </svg>,<年代vg height="11.1" id="M72" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 38.387501 11.1" width="38.387501" 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pan> <tspan style="font-size: 12.50px; " x="12.315455" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="24.355844" y="0"> 5</t年代pan> </text> </g> </g> </svg>。线的精确解(<gydF4y2Baa href="https://static.hindawi.com/articles/ijde/volume-2011/231920/figures/231920/">2.14</gydF4y2Baa>)。</tgydF4y2Bad> </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-569d832f9b48829309e6deead15f6a44"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijde/volume-2011/231920/figures/231920.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-569d832f9b48829309e6deead15f6a44 partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijde/volume-2011/231920/thumbnails/231920.fig.003_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-569d832f9b48829309e6deead15f6a44 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pan> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijde/2011/231920/fig3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> <tbody> <tr> <td>绝对误差<年代vg height="22.362499" id="M73" style="vertical-align:-5.84473pt" version="1.1" viewbox="0 0 75.525002 22.362499" width="75.525002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,22.3625)"> <g transform="translate(72,-54.11)"> <text transform="matrix(1,0,0,-1,-71.95,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5006001" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-59.26,66.03)"> <tspan style="font-size: 8.75px; " x="-1.37" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-43.94,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-26.67,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-14.13,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> </text> </g> </g> </svg>数值方法的考虑数据的问题<gydF4y2Baa href="//www.newsama.com/journals/ijde/2011/fig1/">1</gydF4y2Baa>和<gydF4y2Baa href="//www.newsama.com/journals/ijde/2011/fig2/">2</gydF4y2Baa>在<年代vg height="10.9125" id="M74" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 35.924999 10.9125" width="35.924999" 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pan> <tspan style="font-size: 12.50px; " x="10.339981" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.380369" y="0"> 0</t年代pan> </text> </g> </g> </svg>。广场:<年代vg height="14.6" id="M75" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 41.362499 14.6" width="41.362499" 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pan> </text> <text transform="matrix(1,0,0,-1,-65.6,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.25,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> </text> </g> </g> </svg>;圈:<年代vg height="14.6" id="M76" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 53.525002 14.6" width="53.525002" 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pan> </text> <text transform="matrix(1,0,0,-1,-65.6,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.25,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="21.75522" y="0"> 2</t年代pan> </text> </g> </g> </svg>;空心符号:<年代vg height="14.6" id="M77" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 41.362499 14.6" width="41.362499" 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pan> </text> <text transform="matrix(1,0,0,-1,-65.6,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.25,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> </text> </g> </g> </svg>;填充符号:<年代vg height="14.6" id="M78" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 53.525002 14.6" width="53.525002" 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pan> </text> <text transform="matrix(1,0,0,-1,-65.6,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.25,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="21.75522" y="0"> 2</t年代pan> </text> </g> </g> </svg>。</tgydF4y2Bad> </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-517f5d2fe290c3a4d255106c72b73a13"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijde/volume-2011/231920/figures/231920.fig.004.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-517f5d2fe290c3a4d255106c72b73a13 partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijde/volume-2011/231920/thumbnails/231920.fig.004_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-517f5d2fe290c3a4d255106c72b73a13 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pan> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijde/2011/231920/fig4/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> <tbody> <tr> <td>错误<年代vg height="22.362499" id="M79" style="vertical-align:-5.84473pt" version="1.1" viewbox="0 0 69.275002 22.362499" width="69.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,22.3625)"> <g transform="translate(72,-54.11)"> <text transform="matrix(1,0,0,-1,-71.95,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-61.76,66.03)"> <tspan style="font-size: 8.75px; " x="-1.38" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-46.44,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-29.17,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> </g> </g> </svg>数值方法的问题被认为是数字<gydF4y2Baa href="//www.newsama.com/journals/ijde/2011/fig1/">1</gydF4y2Baa>和<gydF4y2Baa href="//www.newsama.com/journals/ijde/2011/fig2/">2</gydF4y2Baa>在<年代vg height="11.1" id="M80" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 47.650002 11.1" width="47.650002" 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pan> <tspan style="font-size: 12.50px; " x="10.339981" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.380369" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="28.63187" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="31.75762" y="0"> 5</t年代pan> </text> </g> </g> </svg>。广场:<年代vg height="14.6" id="M81" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 41.362499 14.6" width="41.362499" 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pan> </text> <text transform="matrix(1,0,0,-1,-65.6,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.25,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> </text> </g> </g> </svg>;圈:<年代vg height="14.6" id="M82" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 53.525002 14.6" width="53.525002" 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pan> </text> <text transform="matrix(1,0,0,-1,-65.6,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.25,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="21.75522" y="0"> 2</t年代pan> </text> </g> </g> </svg>;空心符号:<年代vg height="14.6" id="M83" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 41.362499 14.6" width="41.362499" 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pan> </text> <text transform="matrix(1,0,0,-1,-65.6,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.25,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> </text> </g> </g> </svg>;填充符号:<年代vg height="14.6" id="M84" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 53.525002 14.6" width="53.525002" 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pan> </text> <text transform="matrix(1,0,0,-1,-65.6,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.25,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="21.75522" y="0"> 2</t年代pan> </text> </g> </g> </svg>。</tgydF4y2Bad> </tr> </tbody> </table> </div> </div> </div> </div> <h4 id="stability">3所示。稳定</gydF4y2Bah4> <p>像往常一样显式方法,目前的显式差分格式(<gydF4y2Baa href="#EEq14">2.12</gydF4y2Baa>)不是无条件稳定,也就是说,对于任意给定的一组值<年代vg height="10.925" id="M85" style="vertical-align:-3.13504pt;width:14.1625px;" version="1.1" viewbox="0 0 14.1625 10.925" width="14.1625" 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pan> </text> <text transform="matrix(1,0,0,-1,-65.6,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg>,<年代vg height="10.925" id="M86" style="vertical-align:-3.13504pt;width:14.1625px;" version="1.1" viewbox="0 0 14.1625 10.925" width="14.1625" 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pan> </text> <text transform="matrix(1,0,0,-1,-65.6,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>,<年代vg height="9.6750002" id="M87" 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pan> </text> </g> </g> </svg>,<年代vg height="10.325" id="M88" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" 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pan> </text> </g> </g> </svg>有选择的<年代vg height="10.8" id="M89" style="vertical-align:-0.11285pt;width:20px;" version="1.1" viewbox="0 0 20 10.8" width="20" 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pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代pan> </text> </g> </g> </svg>和<年代vg height="10.8" id="M90" 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pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代pan> </text> </g> </g> </svg>的方法是不稳定的。因此,重要的是要确定方法的条件是稳定的。为此,我们应当采用分级冯诺依曼稳定性分析(或傅里叶分析)提出(<gydF4y2Baa href="#B32">32</gydF4y2Baa>)(参见[<gydF4y2Baa href="#B34">33</gydF4y2Baa>- - - - - -<gydF4y2Baa href="#B36">35</gydF4y2Baa>])。我们解决的问题是这个过程是在多大程度上有效部分扩散方程,涉及部分衍生品的顺序不同。</gydF4y2Bap> <p>程序(<gydF4y2Baa href="#B32">32</gydF4y2Baa>),我们开始认识到我们的问题的解决方案可以写成subdiffusive的线性组合模式,<年代vg height="22.362499" id="M91" style="vertical-align:-5.84473pt;width:123.7625px;" version="1.1" viewbox="0 0 123.7625 22.362499" width="123.7625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,22.3625)"> <g transform="translate(72,-54.11)"> <text transform="matrix(1,0,0,-1,-71.95,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-66.02,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-50.01,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="0.02"> ∑</t年代pan> </text> <text transform="matrix(1,0,0,-1,-26.54,56.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-19.6,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-12.91,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="8.71"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-0.37,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,5.19,64.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="6.730288" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="10.134816" y="0"> Δ</t年代pan> <tspan style="font-size: 8.75px; " x="16.45376" y="0"> </t年代pan> </text> </g> </g> </svg>,和所有波数<年代vg height="9.875" id="M92" style="vertical-align:-2.29482pt;width:7.9124999px;" version="1.1" viewbox="0 0 7.9124999 9.875" width="7.9124999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.875)"> <g transform="translate(72,-64.1)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>支持的晶格。因此,冯·诺依曼的想法后,我们减少问题的分析解决方案的稳定性分析问题的稳定性的一个通用subdiffusion模式,<年代vg height="16.7125" id="M93" style="vertical-align:-2.29482pt;width:58.325001px;" version="1.1" viewbox="0 0 58.325001 16.7125" width="58.325001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.7125)"> <g transform="translate(72,-58.63)"> <text transform="matrix(1,0,0,-1,-71.95,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.26,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-52.72,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-47.16,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="6.730288" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="10.134816" y="0"> Δ</t年代pan> <tspan style="font-size: 8.75px; " x="16.45376" y="0"> </t年代pan> </text> </g> </g> </svg>。这个表达式插入(<gydF4y2Baa href="#EEq14">2.12</gydF4y2Baa>)一个人<年代pan class="equation" id="eq1"> <svg height="48.387501" id="M94" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.387501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.3875)"> <g transform="translate(72,-33.29)"> <text transform="matrix(1,0,0,-1,3.35,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,10.03,54.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> +</t年代pan> <tspan style="font-size: 8.75px; " x="15.123456" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="19.499456" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,36.42,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,55.15,54.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,70.47,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,95.78,65.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,90.81,43.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,91.33,35.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.7435842" y="0"> =</t年代pan> <tspan style="font-size: 8.75px; " x="10.738704" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,106.97,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,115.48,56.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="13.285536" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,133.21,54.17)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,136.84,56.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 8.75px; " x="-21.360001" y="11.33"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,142.33,47.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,153.75,54.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="6.730288" y="0"> Δ</t年代pan> <tspan style="font-size: 8.75px; " x="13.049232" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,174.89,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="20.367388" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="31.707607" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,212.17,54.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="8.7169924" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="12.725408" y="0"> Δ</t年代pan> <tspan style="font-size: 8.75px; " x="19.044352" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,236.52,47.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.9400001" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,251.15,54.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="15.123456" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="19.867041" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,277.21,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,296.16,54.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,301.04,49.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.104103" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,322.31,54.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,326.75,52.66)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,335.84,65.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,330.87,43.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,331.39,35.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.7435842" y="0"> =</t年代pan> <tspan style="font-size: 8.75px; " x="10.738704" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,347.03,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,355.54,56.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="13.285536" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,373.27,54.17)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,376.9,56.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 8.75px; " x="-21.360001" y="11.33"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,380.31,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,387,54.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="15.123456" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="19.867041" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,410.28,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="54.470001" y="0.15000001"> (</t年代pan> <tspan style="font-size: 12.50px; " x="58.633499" y="0.15000001"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="64.885002" y="0.15000001"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="68.01075" y="0.15000001"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="74.262253" y="0.15000001"> )</t年代pan> </text> </g> </g> </svg></span>稳定的模式是由行为的决定<年代vg height="16.7125" id="M95" style="vertical-align:-2.29482pt;width:24.1625px;" version="1.1" viewbox="0 0 24.1625 16.7125" width="24.1625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.7125)"> <g transform="translate(72,-58.63)"> <text transform="matrix(1,0,0,-1,-71.95,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.26,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> </g> </g> </svg>。写作<年代pan class="equation" id="EEq18"> <svg height="18.549999" id="M96" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 18.549999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.55)"> <g transform="translate(72,-57.16)"> <text transform="matrix(1,0,0,-1,173.18,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,179.87,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> +</t年代pan> <tspan style="font-size: 8.75px; " x="15.123456" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="19.499456" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,206.26,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="18.066835" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,231.03,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,464.75,61.46)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="13.540749" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> )</t年代pan> </text> </g> </g> </svg></span>并假设放大系数<年代vg height="13.425" id="M97" style="vertical-align:-2.29482pt;width:7.6750002px;" version="1.1" viewbox="0 0 7.6750002 13.425" width="7.6750002" 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pan> </text> </g> </g> </svg>subdiffusive模式是独立的时间,我们得到的<年代pan class="equation" id="EEq19"> <svg height="48.387501" id="M98" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.387501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.3875)"> <g transform="translate(72,-33.29)"> <text transform="matrix(1,0,0,-1,34.31,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.5022802" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="21.542669" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="30.569836" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="41.910057" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,90.2,65.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,85.23,43.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,85.75,35.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.7435842" y="0"> =</t年代pan> <tspan style="font-size: 8.75px; " x="10.738704" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,101.39,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,109.9,56.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="13.285536" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,127.63,54.17)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,131.26,56.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 8.75px; " x="-21.360001" y="11.33"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,136.75,47.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8600001" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,148.17,54.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="6.730288" y="0"> Δ</t年代pan> <tspan style="font-size: 8.75px; " x="13.049232" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,169.31,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="20.367388" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="31.707607" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,206.59,54.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="8.7169924" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="12.725408" y="0"> Δ</t年代pan> <tspan style="font-size: 8.75px; " x="19.044352" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,230.95,47.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.9299998" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,244.92,54.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,258.94,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,277.89,54.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,282.77,49.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.104103" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,304.04,54.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,308.48,52.66)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,317.57,65.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,312.6,43.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,313.12,35.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.7435842" y="0"> =</t年代pan> <tspan style="font-size: 8.75px; " x="10.738704" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,328.76,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,337.27,56.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="13.285536" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,355,54.17)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,358.63,56.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 8.75px; " x="-21.360001" y="11.33"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,362.04,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,368.08,54.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,379.32,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="85.43" y="0.15000001"> (</t年代pan> <tspan style="font-size: 12.50px; " x="89.593498" y="0.15000001"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="95.845001" y="0.15000001"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="98.970749" y="0.15000001"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="105.22225" y="0.15000001"> )</t年代pan> </text> </g> </g> </svg></span>如果<年代vg height="13.55" id="M99" style="vertical-align:-2.29482pt;width:41.125px;" version="1.1" viewbox="0 0 41.125 13.55" width="41.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5006001" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.5270462" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="14.50348" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="26.543869" y="0"> 1</t年代pan> </text> </g> </g> </svg>对于一些<年代vg height="9.875" id="M100" style="vertical-align:-2.29482pt;width:7.9124999px;" version="1.1" viewbox="0 0 7.9124999 9.875" width="7.9124999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.875)"> <g transform="translate(72,-64.1)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>解决方案的时间因素,无穷(出口的增长。,(<gydF4y2Baa href="#EEq18">3.2</gydF4y2Baa>),模式是不稳定的。考虑到极端值<年代vg height="13.55" id="M101" style="vertical-align:-2.29482pt;width:45.587502px;" version="1.1" viewbox="0 0 45.587502 13.55" width="45.587502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.5022802" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="21.542669" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="30.107224" y="0"> 1</t年代pan> </text> </g> </g> </svg>,一个从(<gydF4y2Baa href="#EEq19">3.3</gydF4y2Baa>)数值方法是稳定的,如果这个不等式是适用的:<年代pan class="equation" id="EEq20"> <svg height="50.712502" id="M102" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 50.712502" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,50.7125)"> <g transform="translate(72,-31.43)"> <g> <path d="m 95.68,59.83 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,-1,95.68,48.59)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.465491" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="24.50588" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,129.19,53.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="-0.87" y="8.1999998"> ×</t年代pan> </text> <text transform="matrix(1,0,0,-1,139.38,48.59)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="13.23" y="-10.75"> −</t年代pan> <tspan style="font-size: 12.50px; " x="21.794556" y="-10.75"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="30.82172" y="-10.75"> +</t年代pan> <tspan style="font-size: 12.50px; " x="42.161942" y="-10.75"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,189.16,64.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,194.04,59.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.104103" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,215.31,64.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,219.75,62.33)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,225.96,59.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∑</t年代pan> </text> <text transform="matrix(1,0,0,-1,237.39,65.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.9399996"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.7435842" y="9.9399996"> =</t年代pan> <tspan style="font-size: 8.75px; " x="10.738704" y="9.9399996"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,255.08,59.34)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,263.6,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="13.285536" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,281.33,63.85)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,284.95,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 8.75px; " x="-21.35" y="11.33"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,288.37,59.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="12.728054" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.979553" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,311.51,64.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 152.61,51.71 164.14,0" 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,-1,180.84,36.22)"> <tspan style="font-size: 12.50px; " x="16.9" y="0.02"> ∑</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="8.5645552" y="0"> 4</t年代pan> </text> <text transform="matrix(1,0,0,-1,209.16,42.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.9300003"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.7435842" y="9.9300003"> =</t年代pan> <tspan style="font-size: 8.75px; " x="10.738704" y="9.9300003"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,226.86,36.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,235.37,42.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="13.285536" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,253.11,40.72)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,256.73,42.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 8.75px; " x="-21.360001" y="11.34"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,260.14,36.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="12.728054" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.979553" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,283.29,41.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,317.95,48.59)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="146.8" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="150.9635" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="157.215" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="160.34074" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="166.59225" y="0"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代pan class="equation" id="EEq21"> <svg height="38.575001" id="M103" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 38.575001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,38.575)"> <g transform="translate(72,-41.14)"> <g> <path d="m 154.77,64.69 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,-1,154.77,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.465491" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="24.50588" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="35.583538" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="40.447205" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="43.923038" y="0"> n</t年代pan> </text> <text transform="matrix(1,0,0,-1,207.04,58.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,214,46.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.57" y="-15.63"> </t年代pan> <tspan style="font-size: 12.50px; " x="16.296373" y="-15.63"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="25.32354" y="-15.63"> </t年代pan> </text> <g> <path d="m 224.57,56.57 21.63,0" 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,-1,232.26,44.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="15.14" y="-1.4299999"> </t年代pan> <tspan style="font-size: 12.50px; " x="26.6" y="-8.7600002"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="232.49001" y="-8.7600002"> (</t年代pan> <tspan style="font-size: 12.50px; " x="236.6535" y="-8.7600002"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="242.905" y="-8.7600002"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="246.03075" y="-8.7600002"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="252.28224" y="-8.7600002"> )</t年代pan> </text> </g> </g> </svg></span>如果一个定义<年代vg height="15.4625" id="M104" style="vertical-align:-3.35449pt;width:115.3px;" version="1.1" viewbox="0 0 115.3 15.4625" width="115.3" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.4625)"> <g transform="translate(72,-59.63)"> <text transform="matrix(1,0,0,-1,-71.95,63.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-63.82,59.89)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ×</t年代pan> </text> <text transform="matrix(1,0,0,-1,-54.25,63.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> l</t年代pan> <tspan style="font-size: 12.50px; " x="15.50372" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="18.979553" y="0"> 米</t年代pan> </text> <text transform="matrix(1,0,0,-1,-21.37,59.89)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="7.6755042" y="0"> →</t年代pan> <tspan style="font-size: 8.75px; " x="17.232689" y="0"> ∞</t年代pan> </text> <text transform="matrix(1,0,0,-1,4.47,63.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,13.47,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="-0.87" y="8.1999998"> ×</t年代pan> </text> </g> </g> </svg>,一个人<年代pan class="equation" id="EEq22"> <svg height="50.712502" id="M105" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 50.712502" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,50.7125)"> <g transform="translate(72,-31.43)"> <g> <path d="m 96.42,59.83 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,-1,96.42,48.59)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.465491" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="24.50588" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,129.06,45.46)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ×</t年代pan> </text> <text transform="matrix(1,0,0,-1,138.64,48.59)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="13.23" y="-10.75"> −</t年代pan> <tspan style="font-size: 12.50px; " x="21.794556" y="-10.75"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="30.82172" y="-10.75"> +</t年代pan> <tspan style="font-size: 12.50px; " x="42.161942" y="-10.75"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,188.42,64.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,193.29,59.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.104103" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,214.56,64.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,219.01,62.33)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,225.21,59.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∑</t年代pan> </text> <text transform="matrix(1,0,0,-1,236.64,65.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.9399996"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.7435842" y="9.9399996"> =</t年代pan> <tspan style="font-size: 8.75px; " x="10.738704" y="9.9399996"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,254.34,59.34)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,262.85,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="13.285536" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,280.59,63.85)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,284.21,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 8.75px; " x="-21.360001" y="11.33"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,287.62,59.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="12.728054" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.979553" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,310.77,64.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 151.87,51.71 164.14,0" 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,-1,183.01,36.22)"> <tspan style="font-size: 12.50px; " x="16.9" y="0.02"> ∑</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="8.5645552" y="0"> 4</t年代pan> </text> <text transform="matrix(1,0,0,-1,211.33,42.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.9300003"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.7435842" y="9.9300003"> =</t年代pan> <tspan style="font-size: 8.75px; " x="10.738704" y="9.9300003"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,229.03,36.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,237.55,42.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,252.36,40.72)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,237.55,31.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,256.48,36.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="12.728054" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.979553" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,279.63,41.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,317.2,48.59)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="147.55" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="151.7135" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="157.965" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="161.09074" y="0"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="167.34225" y="0"> )</t年代pan> </text> </g> </g> </svg></span>但从(<gydF4y2Baa href="#EEq6">2。4</gydF4y2Baa>),<年代vg height="10.9125" id="M106" style="vertical-align:-0.17555pt;width:45.837502px;" version="1.1" viewbox="0 0 45.837502 10.9125" width="45.837502" 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pan> <tspan style="font-size: 12.50px; " x="9.7023277" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="21.742718" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="30.307272" y="0"> 1</t年代pan> </text> </g> </g> </svg>我们可以看到,<年代vg height="21.125" id="M107" style="vertical-align:-4.75626pt;width:152.825px;" version="1.1" viewbox="0 0 152.825 21.125" width="152.825" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,21.125)"> <g transform="translate(72,-55.1)"> <text transform="matrix(1,0,0,-1,-71.95,59.87)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∑</t年代pan> </text> <text transform="matrix(1,0,0,-1,-60.52,66.13)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.9399996"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.7435842" y="9.9399996"> =</t年代pan> <tspan style="font-size: 8.75px; " x="10.738704" y="9.9399996"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-44.91,59.9)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="12.728054" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.979553" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-21.77,65.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-16.52,59.9)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-8.01,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="10.78"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="13.285536" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="17.731552" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,16.61,59.9)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,34.9,65.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </t年代pan> </text> </g> </g> </svg>,所以<年代pan class="equation" id="EEq23"> <svg height="37.712502" id="M108" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 37.712502" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,37.7125)"> <g transform="translate(72,-41.83)"> <text transform="matrix(1,0,0,-1,155.12,52.73)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,163.24,49.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ×</t年代pan> </text> <text transform="matrix(1,0,0,-1,172.82,52.73)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="13.23" y="-8.3000002"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,192.3,66.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,196.75,64.01)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,203.65,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,222.6,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,227.48,61.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.104103" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,248.75,66.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,253.19,64.02)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代pan> </text> <g> <path d="m 186.05,55.86 71.26,0" 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,-1,202.05,41.88)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,208.3,47.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> +</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,223.12,44.86)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,226.75,47.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,237.19,44.86)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,258.51,52.73)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="206.24001" y="-1.0599999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="210.4035" y="-1.0599999"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="216.655" y="-1.0599999"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="219.78075" y="-1.0599999"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="226.03224" y="-1.0599999"> )</t年代pan> </text> </g> </g> </svg></span>因此,由于<年代vg height="17.3375" id="M109" style="vertical-align:-1.29163pt;width:40.924999px;" version="1.1" viewbox="0 0 40.924999 17.3375" width="40.924999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.3375)"> <g transform="translate(72,-58.13)"> <text transform="matrix(1,0,0,-1,-71.95,59.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.590281" y="0"> ≤</t年代pan> </text> <g> <path d="m -48.31,70.71 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,-48.31,59.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>,我们发现目前的一个充分条件是稳定的方法<年代vg height="14.75" id="M110" style="vertical-align:-3.35449pt;width:47.450001px;" version="1.1" viewbox="0 0 47.450001 14.75" width="47.450001" 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,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.590281" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="23.630671" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-40.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ×</t年代pan> </text> </g> </g> </svg>。在数据<gydF4y2Baa href="//www.newsama.com/journals/ijde/2011/231920/fig5/" target="_blank">5</gydF4y2Baa>和<gydF4y2Baa href="//www.newsama.com/journals/ijde/2011/231920/fig6/" target="_blank">6</gydF4y2Baa>我们展示问题的两个代表性例子如图<gydF4y2Baa href="//www.newsama.com/journals/ijde/2011/231920/fig2/" target="_blank">2</gydF4y2Baa>但对于两个值<年代vg height="10.725" id="M111" 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pan> </text> </g> </g> </svg>分别大于和小于稳定提供的绑定(<gydF4y2Baa href="#EEq23">3.7</gydF4y2Baa>)。一个看到的价值<年代vg height="10.725" id="M112" 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pan> </text> </g> </g> </svg>一个选择是至关重要的:当<年代vg height="10.725" id="M113" 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pan> </text> </g> </g> </svg>小于<年代vg height="14.75" id="M114" style="vertical-align:-3.35449pt;width:17.9125px;" version="1.1" viewbox="0 0 17.9125 14.75" width="17.9125" 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,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-63.82,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ×</t年代pan> </text> </g> </g> </svg>一个是在稳定地区和得到一个合理的数值解(图<gydF4y2Baa href="//www.newsama.com/journals/ijde/2011/231920/fig5/" target="_blank">5</gydF4y2Baa>);否则一个人显然是不稳定的和荒谬的解决方案(图<gydF4y2Baa href="//www.newsama.com/journals/ijde/2011/231920/fig6/" target="_blank">6</gydF4y2Baa>)。</gydF4y2Bap> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-3c138488e74092004aa5cd64179e6adb"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijde/volume-2011/231920/figures/231920.fig.005.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-3c138488e74092004aa5cd64179e6adb partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijde/volume-2011/231920/thumbnails/231920.fig.005_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-3c138488e74092004aa5cd64179e6adb 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pan> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijde/2011/231920/fig5/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> <tbody> <tr> <td>精确解(行)和数值解(符号)我们提供的部分电缆方程的方法<年代vg height="14.7875" id="M115" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 53.087502 14.7875" width="53.087502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7875)"> <g transform="translate(72,-60.17)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.6,60.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.25,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="21.405136" y="0"> 5</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.7875" id="M116" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 53.087502 14.7875" width="53.087502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7875)"> <g transform="translate(72,-60.17)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.6,60.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.25,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="21.405136" y="0"> 5</t年代pan> </text> </g> </g> </svg>对不同数量的步伐<年代vg height="10.9125" id="M117" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 67.175003 10.9125" width="67.175003" 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pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.367147" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="31.407536" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="37.659035" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="41.134869" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="47.386372" y="0"> 0</t年代pan> </text> </g> </g> </svg>,<年代vg height="14.3375" id="M118" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 64.900002 14.3375" width="64.900002" 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,-71.95,60.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="16.403936" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="28.444324" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="34.695824" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-31,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 5</t年代pan> </text> </g> </g> </svg>,<年代vg height="13.55" id="M119" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 68.137497 13.55" width="68.137497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="36.121166" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="48.161556" y="0"> 1</t年代pan> </text> </g> </g> </svg>,<年代vg height="11.1" id="M120" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 38.387501 11.1" width="38.387501" 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pan> <tspan style="font-size: 12.50px; " x="12.315455" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="24.355844" y="0"> 5</t年代pan> </text> </g> </g> </svg>,<年代vg height="16.75" id="M121" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 162.25 16.75" width="162.25" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.590281" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="23.630671" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="27.794168" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="36.821335" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="40.734776" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-27.04,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-22.6,63.85)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-18.48,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="16.666498" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="23.54315" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,9.23,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,17.58,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="21.405136" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="27.656635" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="33.908134" y="0"> 6</t年代pan> </text> </g> </g> </svg>。因为这种情况下在稳定区域<年代vg height="10.725" id="M122" style="vertical-align:-0.1254pt" 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pan> </text> </g> </g> </svg>小于稳定极限吗<年代vg height="18.1625" id="M123" style="vertical-align:-3.35449pt" version="1.1" viewbox="0 0 276 18.1625" width="276" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.1625)"> <g transform="translate(72,-57.47)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-63.82,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ×</t年代pan> </text> <text transform="matrix(1,0,0,-1,-54.25,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-31.8,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-27.35,63.85)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-20.45,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-1.49,65.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,3.38,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.104103" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,24.65,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,29.09,63.85)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,33.22,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,51.27,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> +</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,66.09,63.85)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,69.71,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,80.15,63.85)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,84.28,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> ≃</t年代pan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="25.918718" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="29.04447" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="35.295967" y="0"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="41.54747" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="49.874466" y="0"> …</t年代pan> </text> </g> </g> </svg>(提供的<gydF4y2Baa href="https://static.hindawi.com/articles/ijde/volume-2011/231920/figures/231920/">3.7</gydF4y2Baa>)。对数刻度上的插图显示了结果。</tgydF4y2Bad> </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-2e4c98ed9d219a5678550b58893a45cc"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijde/volume-2011/231920/figures/231920.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-2e4c98ed9d219a5678550b58893a45cc partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijde/volume-2011/231920/thumbnails/231920.fig.006_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-2e4c98ed9d219a5678550b58893a45cc 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pan> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijde/2011/231920/fig6/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> <tbody> <tr> <td>数值解(圆圈)提供的部分电缆方程显式方法<年代vg height="14.7875" id="M124" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 53.087502 14.7875" width="53.087502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7875)"> <g transform="translate(72,-60.17)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.6,60.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.25,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="21.405136" y="0"> 5</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.7875" id="M125" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 53.087502 14.7875" width="53.087502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7875)"> <g transform="translate(72,-60.17)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.6,60.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.25,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="21.405136" y="0"> 5</t年代pan> </text> </g> </g> </svg>在100年之后步伐<年代vg height="10.9125" id="M126" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 67.175003 10.9125" width="67.175003" 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pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.367147" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="31.407536" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="37.659035" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="41.134869" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="47.386372" y="0"> 0</t年代pan> </text> </g> </g> </svg>,<年代vg height="14.5" id="M127" style="vertical-align:-0.3135pt" version="1.1" viewbox="0 0 101.3875 14.5" width="101.3875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5)"> <g transform="translate(72,-60.4)"> <text transform="matrix(1,0,0,-1,-71.95,60.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="16.403936" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="28.444324" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="34.695824" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="37.821575" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="46.84874" y="0"> ×</t年代pan> <tspan style="font-size: 12.50px; " x="57.626328" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="63.877827" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-1.81,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 5</t年代pan> </text> </g> </g> </svg>,<年代vg height="13.55" id="M128" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 68.137497 13.55" width="68.137497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="36.121166" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="48.161556" y="0"> 1</t年代pan> </text> </g> </g> </svg>,<年代vg height="11.1" id="M129" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 38.387501 11.1" width="38.387501" 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pan> <tspan style="font-size: 12.50px; " x="12.315455" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="24.355844" y="0"> 5</t年代pan> </text> </g> </g> </svg>,<年代vg height="16.75" id="M130" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 149.89999 16.75" width="149.89999" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.590281" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="23.630671" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="27.794168" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="36.821335" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="40.734776" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-27.04,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-22.1,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="16.666498" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="23.54315" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,5.61,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,13.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="18.291889" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="21.417639" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="27.66914" y="0"> 6</t年代pan> </text> </g> </g> </svg>。注意,这个值大于稳定极限<年代vg height="18.1625" id="M131" style="vertical-align:-3.35449pt" version="1.1" viewbox="0 0 276 18.1625" width="276" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.1625)"> <g transform="translate(72,-57.47)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-63.82,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ×</t年代pan> </text> <text transform="matrix(1,0,0,-1,-54.25,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-31.8,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-27.35,63.85)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-20.45,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-1.49,65.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,3.38,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.104103" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,24.65,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,29.09,63.85)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,33.22,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,51.27,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> +</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,66.09,63.85)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,69.71,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,80.15,63.85)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,84.28,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> ≃</t年代pan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="25.918718" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="29.04447" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="35.295967" y="0"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="41.54747" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="49.874466" y="0"> …</t年代pan> </text> </g> </g> </svg>(提供的<gydF4y2Baa href="https://static.hindawi.com/articles/ijde/volume-2011/231920/figures/231920/">3.7</gydF4y2Baa>)。虚线是指导。</tgydF4y2Bad> </tr> </tbody> </table> </div> </div> </div> </div> <h4 id="numerical-check-of-the-stability-analysis">4所示。数值稳定性分析的检查</gydF4y2Bah4> <p>在本节中,我们描述一个全面检查我们的稳定性分析的有效性通过使用许多不同的参数值<年代vg height="10.925" id="M132" style="vertical-align:-3.13504pt;width:14.1625px;" version="1.1" viewbox="0 0 14.1625 10.925" width="14.1625" 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pan> </text> <text transform="matrix(1,0,0,-1,-65.6,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg>,<年代vg height="10.925" id="M133" style="vertical-align:-3.13504pt;width:14.1625px;" version="1.1" viewbox="0 0 14.1625 10.925" width="14.1625" 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pan> </text> <text transform="matrix(1,0,0,-1,-65.6,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>,<年代vg height="10.8" id="M134" 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pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代pan> </text> </g> </g> </svg>,<年代vg height="10.8" id="M135" style="vertical-align:-0.11285pt;width:20px;" version="1.1" viewbox="0 0 20 10.8" width="20" 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pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代pan> </text> </g> </g> </svg>和测试数值方法的稳定性是否预测(<gydF4y2Baa href="#EEq23">3.7</gydF4y2Baa>)。不失一般性,我们假设<年代vg height="13.55" id="M136" style="vertical-align:-2.29482pt;width:68.137497px;" version="1.1" viewbox="0 0 68.137497 13.55" width="68.137497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.077658" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="23.118048" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="36.121166" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="48.161556" y="0"> 1</t年代pan> </text> </g> </g> </svg>在所有情况下。我们以以下方式进行。首先,我们选择的一组值<年代vg height="10.925" id="M137" style="vertical-align:-3.13504pt;width:14.1625px;" version="1.1" viewbox="0 0 14.1625 10.925" width="14.1625" 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pan> </text> <text transform="matrix(1,0,0,-1,-65.6,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg>,<年代vg height="10.925" id="M138" style="vertical-align:-3.13504pt;width:14.1625px;" version="1.1" viewbox="0 0 14.1625 10.925" width="14.1625" 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pan> </text> <text transform="matrix(1,0,0,-1,-65.6,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>,<年代vg height="10.8" id="M139" style="vertical-align:-0.11285pt;width:20px;" version="1.1" viewbox="0 0 20 10.8" width="20" 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pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代pan> </text> </g> </g> </svg>,<年代vg height="10.725" id="M140" 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pan> </text> </g> </g> </svg>和整合相应的部分电缆方程。如果<年代pan class="equation" id="EEq24"> <svg height="20.512501" id="M141" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 20.512501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,20.5125)"> <g transform="translate(72,-55.59)"> <text transform="matrix(1,0,0,-1,165.59,63.38)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="4.6900001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5" y="2.3499999"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,178.28,66.03)"> <tspan style="font-size: 8.75px; " x="-1.38" y="8.7600002"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="6.2139201" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="12.20904" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,198.14,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,219.67,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="-1.37" y="8.7600002"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,226.39,63.38)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="4.6900001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="5.9699998" y="2.3499999"> ></t年代pan> <tspan style="font-size: 12.50px; " x="17.997887" y="2.3499999"> </t年代pan> <tspan style="font-size: 12.50px; " x="238.36" y="2.71"> (</t年代pan> <tspan style="font-size: 12.50px; " x="242.5235" y="2.71"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="248.77499" y="2.71"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="251.90074" y="2.71"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="258.15225" y="2.71"> )</t年代pan> </text> </g> </g> </svg></span>为<年代vg height="10.9375" id="M142" style="vertical-align:-0.20064pt;width:43.599998px;" version="1.1" viewbox="0 0 43.599998 10.9375" width="43.599998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9375)"> <g transform="translate(72,-63.25)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.227454" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.267843" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="28.519342" y="0"> 0</t年代pan> </text> </g> </g> </svg>1000集成在第一,然后我们说,方法是不稳定的;否则,我们标签和稳定的方法。我们生成的图<gydF4y2Baa href="//www.newsama.com/journals/ijde/2011/231920/fig7/" target="_blank">7</gydF4y2Baa>从价值观的整合<年代vg height="10.725" id="M143" 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pan> </text> </g> </g> </svg>远低于理论给出的稳定极限(<gydF4y2Baa href="#EEq23">3.7</gydF4y2Baa>)和保持其价值增加0.001,直到条件(<gydF4y2Baa href="#EEq24">4.1</gydF4y2Baa>第一次到达。最后一个值的方法稳定记录和绘制在图<gydF4y2Baa href="//www.newsama.com/journals/ijde/2011/231920/fig7/" target="_blank">7</gydF4y2Baa>。极限的值<年代vg height="10.9375" id="M144" style="vertical-align:-0.20064pt;width:43.599998px;" version="1.1" viewbox="0 0 43.599998 10.9375" width="43.599998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9375)"> <g transform="translate(72,-63.25)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.227454" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.267843" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="28.519342" y="0"> 0</t年代pan> </text> </g> </g> </svg>是任意的,但选择其他合理值不显著改变这些情节。</gydF4y2Bap> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-b75363e163da30bb69e4bd1df6dd313a"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijde/volume-2011/231920/figures/231920.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-b75363e163da30bb69e4bd1df6dd313a partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijde/volume-2011/231920/thumbnails/231920.fig.007_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-b75363e163da30bb69e4bd1df6dd313a 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pan> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijde/2011/231920/fig7/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> <tbody> <tr> <td>稳定约束<年代vg height="10.725" id="M145" style="vertical-align:-0.1254pt" 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pan> </text> </g> </g> </svg>与<年代vg height="10.925" id="M146" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 14.1625 10.925" width="14.1625" 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pan> </text> <text transform="matrix(1,0,0,-1,-65.6,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg>数的值<年代vg height="10.925" id="M147" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 14.1625 10.925" width="14.1625" 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pan> </text> <text transform="matrix(1,0,0,-1,-65.6,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>在哪里<年代vg height="10.9125" id="M148" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 67.175003 10.9125" width="67.175003" 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pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.367147" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="31.407536" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="37.659035" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="41.134869" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="47.386372" y="0"> 0</t年代pan> </text> </g> </g> </svg>,<年代vg height="13.55" id="M149" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 68.137497 13.55" width="68.137497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.990617" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="25.031006" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="36.121166" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="48.161556" y="0"> 1</t年代pan> </text> </g> </g> </svg>。符号数值估计。行对应的理论预测(<gydF4y2Baa href="https://static.hindawi.com/articles/ijde/volume-2011/231920/figures/231920/">3.7</gydF4y2Baa>)。</tgydF4y2Bad> </tr> </tbody> </table> </div> </div> </div> </div> <h4 id="convergence-analysis">5。收敛性分析</gydF4y2Bah4> <p>在本节中,我们表明,目前的数值方法是收敛的,也就是说,这一数值解收敛到精确解时的大小时空离散化归零。让我们定义<年代vg height="22.362499" id="M150" style="vertical-align:-5.84473pt;width:20.9125px;" version="1.1" viewbox="0 0 20.9125 22.362499" width="20.9125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,22.3625)"> <g transform="translate(72,-54.11)"> <text transform="matrix(1,0,0,-1,-71.95,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-66.39,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="7.658" y="0"> )</t年代pan> </text> </g> </g> </svg>是准确的和数值之间的差异在点的解决方案<年代vg height="16.637501" id="M151" style="vertical-align:-4.77652pt;width:44.462502px;" version="1.1" viewbox="0 0 44.462502 16.637501" width="44.462502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6375)"> <g transform="translate(72,-58.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-60.91,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.48,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-47.36,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-40.65,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> </text> </g> </g> </svg>:<年代vg height="22.362499" id="M152" style="vertical-align:-5.84473pt;width:105.775px;" version="1.1" viewbox="0 0 105.775 22.362499" width="105.775" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,22.3625)"> <g transform="translate(72,-54.11)"> <text transform="matrix(1,0,0,-1,-71.95,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-66.39,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="7.658" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-51.84,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-33.88,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="7.658" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-20.03,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,1.5,66.03)"> <tspan style="font-size: 8.75px; " x="-1.37" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="7.658" y="0"> )</t年代pan> </text> </g> </g> </svg>。考虑到(<gydF4y2Baa href="#EEq11">2。9</gydF4y2Baa>)和(<gydF4y2Baa href="#EEq13">2.11</gydF4y2Baa>),得到了方程描述了这种差异的发展:<年代pan class="equation" id="EEq25"> <svg height="81.837502" id="M153" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 81.837502" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,81.8375)"> <g transform="translate(72,-6.53)"> <text transform="matrix(1,0,0,-1,5.34,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,10.91,55.72)"> <tspan style="font-size: 8.75px; " x="0" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> +</t年代pan> <tspan style="font-size: 8.75px; " x="15.123456" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="19.499456" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,36.6,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,53.5,55.72)"> <tspan style="font-size: 8.75px; " x="0" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,68.82,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,94.14,65.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,89.17,43.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,89.69,35.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.7435842" y="0"> =</t年代pan> <tspan style="font-size: 8.75px; " x="10.738704" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,105.32,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,113.84,56.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="13.285536" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,131.57,54.17)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,135.19,56.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 8.75px; " x="-21.35" y="11.33"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,140.69,44.75)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.3600001" y="-4.9200001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,153.62,55.72)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="15.123456" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="19.867041" y="0"> )</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="10.76"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.4045279" y="10.76"> +</t年代pan> <tspan style="font-size: 8.75px; " x="9.3996477" y="10.76"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,179.68,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="17.579218" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,202.83,55.72)"> <tspan style="font-size: 8.75px; " x="0" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="15.123456" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="19.867041" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,228.89,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,245.8,55.72)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="15.123456" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="19.867041" y="0"> )</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="10.76"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.4045279" y="10.76"> −</t年代pan> <tspan style="font-size: 8.75px; " x="9.3996477" y="10.76"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,269.08,44.75)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.38" y="-4.9200001"> +</t年代pan> <tspan style="font-size: 12.50px; " x="21.720221" y="-4.9200001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,298.42,54.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,303.29,49.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.104103" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,324.56,54.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,329.01,52.66)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,338.1,65.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,333.13,43.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,333.65,35.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.7435842" y="0"> =</t年代pan> <tspan style="font-size: 8.75px; " x="10.738704" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,349.28,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,357.8,56.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="13.285536" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,375.53,54.17)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,379.15,56.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 8.75px; " x="-21.35" y="11.33"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,382.57,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,388.13,55.72)"> <tspan style="font-size: 8.75px; " x="0" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="15.123456" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="19.867041" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,28.74,12.41)"> <tspan style="font-size: 12.50px; " x="23" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="28.85" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,64.47,9.29)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,68.9,12.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,78.02,9.29)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,83.26,9.9)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.3199997" y="-2.51"> ≡</t年代pan> <tspan style="font-size: 12.50px; " x="21.36039" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,113.5,18.46)"> <tspan style="font-size: 8.75px; " x="-2" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,126.04,12.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="338.70999" y="-23.73"> (</t年代pan> <tspan style="font-size: 12.50px; " x="342.8735" y="-23.73"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="349.125" y="-23.73"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="352.25076" y="-23.73"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="358.50226" y="-23.73"> )</t年代pan> </text> </g> </g> </svg></span>正如我们在前一节中所做的一样<年代vg height="22.362499" id="M154" style="vertical-align:-5.84473pt;width:26.700001px;" version="1.1" viewbox="0 0 26.700001 22.362499" width="26.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,22.3625)"> <g transform="translate(72,-54.11)"> <text transform="matrix(1,0,0,-1,-71.95,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-61.76,66.03)"> <tspan style="font-size: 8.75px; " x="-1.38" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="7.658" y="0"> )</t年代pan> </text> </g> </g> </svg>,我们写<年代vg height="22.362499" id="M155" style="vertical-align:-5.84473pt;width:20.9125px;" version="1.1" viewbox="0 0 20.9125 22.362499" width="20.9125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,22.3625)"> <g transform="translate(72,-54.11)"> <text transform="matrix(1,0,0,-1,-71.95,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-66.39,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="7.658" y="0"> )</t年代pan> </text> </g> </g> </svg>和<年代vg height="22.362499" id="M156" style="vertical-align:-5.84473pt;width:26.9px;" version="1.1" viewbox="0 0 26.9 22.362499" width="26.9" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,22.3625)"> <g transform="translate(72,-54.11)"> <text transform="matrix(1,0,0,-1,-71.95,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-63.07,66.03)"> <tspan style="font-size: 8.75px; " x="-2" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> </g> </g> </svg>(子)扩散的组合模式,<年代vg height="22.362499" id="M157" style="vertical-align:-5.84473pt;width:119.625px;" version="1.1" viewbox="0 0 119.625 22.362499" width="119.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,22.3625)"> <g transform="translate(72,-54.11)"> <text transform="matrix(1,0,0,-1,-71.95,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-66.39,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="7.658" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-51.84,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="0.02"> ∑</t年代pan> </text> <text transform="matrix(1,0,0,-1,-28.38,56.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-21.44,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-14.75,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="8.71"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="7.658" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-3.68,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,1.89,64.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="6.730288" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="10.134816" y="0"> Δ</t年代pan> <tspan style="font-size: 8.75px; " x="16.45376" y="0"> </t年代pan> </text> </g> </g> </svg>和<年代vg height="22.362499" id="M158" style="vertical-align:-5.84473pt;width:129.78751px;" version="1.1" viewbox="0 0 129.78751 22.362499" width="129.78751" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,22.3625)"> <g transform="translate(72,-54.11)"> <text transform="matrix(1,0,0,-1,-71.95,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-63.07,66.03)"> <tspan style="font-size: 8.75px; " x="-2" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-47.06,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="0.02"> ∑</t年代pan> </text> <text transform="matrix(1,0,0,-1,-23.59,56.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-16.65,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-8.09,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="8.71"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,4.45,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,10.02,64.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="6.730288" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="10.134816" y="0"> Δ</t年代pan> <tspan style="font-size: 8.75px; " x="16.45376" y="0"> </t年代pan> </text> </g> </g> </svg>和分析单个的收敛,但通用的<年代vg height="9.875" id="M159" style="vertical-align:-2.29482pt;width:7.9124999px;" version="1.1" viewbox="0 0 7.9124999 9.875" width="7.9124999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.875)"> <g transform="translate(72,-64.1)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>模式(<gydF4y2Baa href="#B37">36</gydF4y2Baa>,<gydF4y2Baa href="#B40">39</gydF4y2Baa>,<gydF4y2Baa href="#B41">42</gydF4y2Baa>]。因此,取代<年代vg height="22.362499" id="M160" style="vertical-align:-5.84473pt;width:20.9125px;" version="1.1" viewbox="0 0 20.9125 22.362499" width="20.9125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,22.3625)"> <g transform="translate(72,-54.11)"> <text transform="matrix(1,0,0,-1,-71.95,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-66.39,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="7.658" y="0"> )</t年代pan> </text> </g> </g> </svg>通过<年代vg height="16.7125" id="M161" style="vertical-align:-2.29482pt;width:56.487499px;" version="1.1" viewbox="0 0 56.487499 16.7125" width="56.487499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.7125)"> <g transform="translate(72,-58.63)"> <text transform="matrix(1,0,0,-1,-71.95,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.26,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="7.658" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-54.19,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-48.63,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="6.730288" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="10.134816" y="0"> Δ</t年代pan> <tspan style="font-size: 8.75px; " x="16.45376" y="0"> </t年代pan> </text> </g> </g> </svg>和<年代vg height="22.362499" id="M162" style="vertical-align:-5.84473pt;width:26.9px;" version="1.1" viewbox="0 0 26.9 22.362499" width="26.9" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,22.3625)"> <g transform="translate(72,-54.11)"> <text transform="matrix(1,0,0,-1,-71.95,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-63.07,66.03)"> <tspan style="font-size: 8.75px; " x="-2" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> </g> </g> </svg>通过<年代vg height="16.924999" id="M163" style="vertical-align:-2.53308pt;width:60.674999px;" version="1.1" viewbox="0 0 60.674999 16.924999" width="60.674999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.925)"> <g transform="translate(72,-58.46)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-63.39,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-50.84,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-45.28,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="6.730288" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="10.134816" y="0"> Δ</t年代pan> <tspan style="font-size: 8.75px; " x="16.45376" y="0"> </t年代pan> </text> </g> </g> </svg>在(<gydF4y2Baa href="#EEq25">5.1</gydF4y2Baa>),我们得到<年代pan class="equation" id="EEq26"> <svg height="48.387501" id="M164" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.387501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.3875)"> <g transform="translate(72,-33.29)"> <text transform="matrix(1,0,0,-1,37.84,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,44.53,54.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> +</t年代pan> <tspan style="font-size: 8.75px; " x="15.123456" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="19.499456" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,70.91,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,89.64,54.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,104.96,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> </text> <g> <path d="m 116.3,60.91 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,-1,116.3,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,130.27,65.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,125.3,43.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,125.82,35.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.7435842" y="0"> =</t年代pan> <tspan style="font-size: 8.75px; " x="10.738704" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,141.46,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,149.97,56.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="13.285536" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,167.7,54.17)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,171.33,56.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 8.75px; " x="-21.360001" y="11.33"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,174.74,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,181.43,54.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="15.123456" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="19.867041" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,207.49,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,226.45,54.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,231.32,49.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.104103" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,252.59,54.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,257.03,52.66)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,266.13,65.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,261.16,43.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,261.67,35.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.7435842" y="0"> =</t年代pan> <tspan style="font-size: 8.75px; " x="10.738704" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,277.31,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,285.82,56.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="13.285536" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,303.56,54.17)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,307.18,56.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 8.75px; " x="-21.360001" y="11.33"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,310.59,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,317.28,54.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="15.123456" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="19.867041" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,343.34,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,363.25,54.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,375.79,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="88.959999" y="0.15000001"> (</t年代pan> <tspan style="font-size: 12.50px; " x="93.123497" y="0.15000001"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="99.375" y="0.15000001"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="102.50075" y="0.15000001"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="108.75225" y="0.15000001"> )</t年代pan> </text> </g> </g> </svg></span></p> <p>现在我们将用归纳法证明<年代vg height="16.8375" id="M165" style="vertical-align:-2.29482pt;width:153.6125px;" version="1.1" viewbox="0 0 153.6125 16.8375" width="153.6125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.8375)"> <g transform="translate(72,-58.53)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5006001" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.76,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-50.22,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="5.9639311" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="18.00432" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="27.156515" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="31.320015" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="40.347179" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="44.26062" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="51.199783" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="62.552509" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="71.954765" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="76.118263" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="85.145432" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="92.022079" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,45.97,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>对所有<年代vg height="7.1374998" id="M166" 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pan> </text> </g> </g> </svg>。首先,<年代vg height="22.362499" id="M167" style="vertical-align:-5.84473pt;width:26.237499px;" version="1.1" viewbox="0 0 26.237499 22.362499" width="26.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,22.3625)"> <g transform="translate(72,-54.11)"> <text transform="matrix(1,0,0,-1,-71.95,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-61.76,66.03)"> <tspan style="font-size: 8.75px; " x="-1.38" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 0</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> </g> </g> </svg>满足初始条件的建设,所以<年代vg height="22.362499" id="M168" style="vertical-align:-5.84473pt;width:47.662498px;" version="1.1" viewbox="0 0 47.662498 22.362499" width="47.662498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,22.3625)"> <g transform="translate(72,-54.11)"> <text transform="matrix(1,0,0,-1,-71.95,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-66.39,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 0</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-52.21,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代pan> </text> </g> </g> </svg>。这意味着<年代vg height="16.7125" id="M169" style="vertical-align:-2.29482pt;width:49.0625px;" version="1.1" viewbox="0 0 49.0625 16.7125" width="49.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.7125)"> <g transform="translate(72,-58.63)"> <text transform="matrix(1,0,0,-1,-71.95,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.26,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 0</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-51.08,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代pan> </text> </g> </g> </svg>。因此,从(<gydF4y2Baa href="#EEq26">5.2</gydF4y2Baa>)一个人<年代vg height="17.012501" id="M170" style="vertical-align:-2.53308pt;width:65.337502px;" version="1.1" viewbox="0 0 65.337502 17.012501" width="65.337502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.0125)"> <g transform="translate(72,-58.39)"> <text transform="matrix(1,0,0,-1,-71.95,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.26,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-51.08,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-30.48,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 0</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> </g> </g> </svg>。但从(<gydF4y2Baa href="#EEq12">2.10</gydF4y2Baa>人知道,<年代vg height="22.362499" id="M171" style="vertical-align:-5.84473pt;width:203.77499px;" version="1.1" viewbox="0 0 203.77499 22.362499" width="203.77499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,22.3625)"> <g transform="translate(72,-54.11)"> <text transform="matrix(1,0,0,-1,-71.95,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5006001" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-60.57,66.03)"> <tspan style="font-size: 8.75px; " x="-2" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 0</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-49.87,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="5.9639311" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="18.00432" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="20.504919" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-20.79,64.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 0</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-10.09,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="5.9639311" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="18.00432" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="27.156515" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="31.320015" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="40.347179" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="44.26062" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="51.199783" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="62.552509" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="71.954765" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="76.118263" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="85.145432" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="92.022079" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,86.1,65.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>,所以<年代vg height="16.8375" id="M172" style="vertical-align:-2.29482pt;width:151.3125px;" version="1.1" viewbox="0 0 151.3125 16.8375" width="151.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.8375)"> <g transform="translate(72,-58.53)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5006001" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.76,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-52.06,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="5.9639311" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="18.00432" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="27.156515" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="31.320015" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="40.347179" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="44.26062" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="51.199783" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="62.552509" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="71.954765" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="76.118263" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="85.145432" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="92.022079" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,44.13,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>。现在让我们假设<年代vg height="16.8375" id="M173" style="vertical-align:-2.29482pt;width:151.77499px;" version="1.1" viewbox="0 0 151.77499 16.8375" width="151.77499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.8375)"> <g transform="translate(72,-58.53)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5006001" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.76,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="7.658" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-51.69,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="5.9639311" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="18.00432" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="27.156515" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="31.320015" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="40.347179" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="44.26062" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="51.199783" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="62.552509" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="71.954765" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="76.118263" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="85.145432" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="92.022079" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,44.5,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>适用于<年代vg height="12.8875" id="M174" style="vertical-align:-1.76814pt;width:78.150002px;" version="1.1" viewbox="0 0 78.150002 12.8875" width="78.150002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.8875)"> <g transform="translate(72,-61.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.239957" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.280346" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="28.531845" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="33.745598" y="0"> …</t年代pan> <tspan style="font-size: 12.50px; " x="48.324097" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="53.537846" y="0"> </t年代pan> </text> </g> </g> </svg>。然后我们将证明<年代vg height="16.8375" id="M175" style="vertical-align:-2.29482pt;width:166.575px;" version="1.1" viewbox="0 0 166.575 16.8375" width="166.575" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.8375)"> <g transform="translate(72,-58.53)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5006001" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.76,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> +</t年代pan> <tspan style="font-size: 8.75px; " x="15.123456" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="19.499456" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-39.85,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="5.9639311" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="18.00432" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="27.156515" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="31.320015" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="40.347179" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="44.26062" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="51.199783" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="62.552509" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="71.954765" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="76.118263" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="85.145432" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="92.022079" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,56.34,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>。从(<gydF4y2Baa href="#EEq26">5.2</gydF4y2Baa>我们获得<年代pan class="equation" id="EEq27"> <svg height="48.387501" id="M176" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.387501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.3875)"> <g transform="translate(72,-33.29)"> <text transform="matrix(1,0,0,-1,21.2,51.43)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.5"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.51" y="1.76"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,30.39,54.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> +</t年代pan> <tspan style="font-size: 8.75px; " x="15.123456" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="19.499456" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,53.31,51.43)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.5"> |</t年代pan> <tspan style="font-size: 12.50px; " x="5.9699998" y="1.76"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="20.09" y="0.059999999"> |</t年代pan> <tspan style="font-size: 12.50px; " x="20.09" y="3.4400001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="22.59" y="1.76"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,84.47,54.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,97.01,51.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.3800001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="5.2800002" y="1.7"> +</t年代pan> <tspan style="font-size: 12.50px; " x="16.620001" y="-0.059999999"> |</t年代pan> <tspan style="font-size: 12.50px; " x="16.620001" y="3.4400001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="19.120001" y="1.7"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,122.82,54.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,135.36,51.43)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.5"> |</t年代pan> <tspan style="font-size: 12.50px; " x="5.2800002" y="1.76"> +</t年代pan> </text> <g> <path d="m 151.98,60.91 9.01,0" 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,-1,151.98,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.09" y="-1.79"> |</t年代pan> <tspan style="font-size: 12.50px; " x="11.09" y="1.77"> |</t年代pan> <tspan style="font-size: 12.50px; " x="13.59" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,172.26,54.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> {</t年代pan> <tspan style="font-size: 8.75px; " x="4.2009602" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="10.41488" y="0"> }</t年代pan> </text> <text transform="matrix(1,0,0,-1,187.37,51.46)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.5599999"> |</t年代pan> </text> <text transform="matrix(1,0,0,-1,196.93,65.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,191.96,43.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,192.48,35.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.7435842" y="0"> =</t年代pan> <tspan style="font-size: 8.75px; " x="10.738704" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,210.2,56.59)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="10.66"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="13.82"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5" y="6.9200001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,221.21,56.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="13.285536" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,238.94,54.17)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,242.57,56.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 8.75px; " x="-21.360001" y="11.33"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,245.98,56.59)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="10.66"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="13.82"> |</t年代pan> <tspan style="font-size: 12.50px; " x="5.2800002" y="6.9200001"> −</t年代pan> <tspan style="font-size: 12.50px; " x="16.62022" y="6.9200001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,270.22,54.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,275.09,49.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.104103" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,296.36,54.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,300.8,52.66)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,307.01,51.46)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.5599999"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5" y="1.79"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,316.2,54.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> {</t年代pan> <tspan style="font-size: 8.75px; " x="4.2009602" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="10.41488" y="0"> }</t年代pan> </text> <text transform="matrix(1,0,0,-1,331.31,51.46)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.5599999"> |</t年代pan> </text> <text transform="matrix(1,0,0,-1,340.87,65.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,335.9,43.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,336.42,35.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.7435842" y="0"> =</t年代pan> <tspan style="font-size: 8.75px; " x="10.738704" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,354.14,56.59)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="10.66"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="13.82"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5" y="6.9200001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,365.15,56.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="13.285536" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,382.88,54.17)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,386.51,56.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 8.75px; " x="-21.360001" y="11.33"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,389.92,56.59)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="10.66"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="13.82"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5" y="7.0700002"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="74.830002" y="7.0700002"> (</t年代pan> <tspan style="font-size: 12.50px; " x="78.9935" y="7.0700002"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="85.245003" y="7.0700002"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="88.37075" y="7.0700002"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="94.622246" y="7.0700002"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="16.762501" id="M177" style="vertical-align:-2.29482pt;width:33.625px;" version="1.1" viewbox="0 0 33.625 16.762501" width="33.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.7625)"> <g transform="translate(72,-58.59)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5006001" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.76,66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> {</t年代pan> <tspan style="font-size: 8.75px; " x="4.2009602" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="10.41488" y="0"> }</t年代pan> </text> <text transform="matrix(1,0,0,-1,-47.65,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> </text> </g> </g> </svg>的最大价值<年代vg height="16.7125" id="M178" style="vertical-align:-2.29482pt;width:28.575001px;" version="1.1" viewbox="0 0 28.575001 16.7125" width="28.575001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.7125)"> <g transform="translate(72,-58.63)"> <text transform="matrix(1,0,0,-1,-71.95,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5006001" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.76,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="7.658" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-51.69,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> </text> </g> </g> </svg>为<年代vg height="12.8875" id="M179" style="vertical-align:-1.76814pt;width:78.150002px;" version="1.1" viewbox="0 0 78.150002 12.8875" width="78.150002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.8875)"> <g transform="translate(72,-61.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.239957" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.280346" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="28.531845" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="33.745598" y="0"> …</t年代pan> <tspan style="font-size: 12.50px; " x="48.324097" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="53.537846" y="0"> </t年代pan> </text> </g> </g> </svg>。考虑到(<gydF4y2Baa href="#EEq6">2。4</gydF4y2Baa>),使用价值<年代vg height="10.9125" id="M180" style="vertical-align:-0.17555pt;width:35.125px;" version="1.1" viewbox="0 0 35.125 10.9125" width="35.125" 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pan> <tspan style="font-size: 12.50px; " x="9.7023277" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="21.742718" y="0"> 1</t年代pan> </text> </g> </g> </svg>,因为<年代vg height="21.125" id="M181" style="vertical-align:-4.85281pt;width:52.049999px;" version="1.1" viewbox="0 0 52.049999 21.125" width="52.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,21.125)"> <g transform="translate(72,-55.1)"> <text transform="matrix(1,0,0,-1,-71.95,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-63.44,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="10.76"> 0</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="7.850544" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-48.7,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> </text> </g> </g> </svg>,很容易看到<年代vg height="21.012501" id="M182" style="vertical-align:-4.75626pt;width:99.162498px;" version="1.1" viewbox="0 0 99.162498 21.012501" width="99.162498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,21.0125)"> <g transform="translate(72,-55.19)"> <text transform="matrix(1,0,0,-1,-71.95,59.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∑</t年代pan> </text> <text transform="matrix(1,0,0,-1,-60.52,66.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.9399996"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.7435842" y="9.9399996"> =</t年代pan> <tspan style="font-size: 8.75px; " x="10.738704" y="9.9399996"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-42.83,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-34.31,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="10.69"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="7.8417921" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-19.57,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="20.592442" y="0"> 1</t年代pan> </text> </g> </g> </svg>或者,同样,<年代vg height="21.012501" id="M183" style="vertical-align:-4.75626pt;width:94.712502px;" version="1.1" viewbox="0 0 94.712502 21.012501" width="94.712502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,21.0125)"> <g transform="translate(72,-55.19)"> <text transform="matrix(1,0,0,-1,-71.95,59.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∑</t年代pan> </text> <text transform="matrix(1,0,0,-1,-60.52,66.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.9399996"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.7435842" y="9.9399996"> =</t年代pan> <tspan style="font-size: 8.75px; " x="10.738704" y="9.9399996"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-42.83,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5006001" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-31.81,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="10.69"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="7.8417921" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-20.55,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="5.9764342" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="18.00432" y="0"> 1</t年代pan> </text> </g> </g> </svg>自<年代vg height="21.012501" id="M184" style="vertical-align:-4.75626pt;width:52.049999px;" version="1.1" viewbox="0 0 52.049999 21.012501" width="52.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,21.0125)"> <g transform="translate(72,-55.19)"> <text transform="matrix(1,0,0,-1,-71.95,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-63.44,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="10.69"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="7.850544" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-48.7,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代pan> </text> </g> </g> </svg>为<年代vg height="12.3" id="M185" style="vertical-align:-1.29163pt;width:35.799999px;" version="1.1" viewbox="0 0 35.799999 12.3" width="35.799999" 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pan> <tspan style="font-size: 12.50px; " x="10.239957" y="0"> ≥</t年代pan> <tspan style="font-size: 12.50px; " x="22.280346" y="0"> 1</t年代pan> </text> </g> </g> </svg>(见(<gydF4y2Baa href="#EEq4">2。3</gydF4y2Baa>))。因此<年代vg height="21.125" id="M186" style="vertical-align:-4.75626pt;width:79.849998px;" version="1.1" viewbox="0 0 79.849998 21.125" width="79.849998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,21.125)"> <g transform="translate(72,-55.1)"> <text transform="matrix(1,0,0,-1,-71.95,59.87)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∑</t年代pan> </text> <text transform="matrix(1,0,0,-1,-60.52,66.13)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.9399996"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.7435842" y="9.9399996"> =</t年代pan> <tspan style="font-size: 8.75px; " x="10.738704" y="9.9399996"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-42.83,59.9)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5006001" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-31.81,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="10.78"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="13.285536" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="17.722799" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-10.67,59.9)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> </text> </g> </g> </svg>是有界的(事实上,它小于2)。使用这个结果(<gydF4y2Baa href="#EEq27">5.3</gydF4y2Baa>),与<年代vg height="16.8375" id="M187" style="vertical-align:-2.29482pt;width:139.075px;" version="1.1" viewbox="0 0 139.075 16.8375" width="139.075" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.8375)"> <g transform="translate(72,-58.53)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5006001" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.76,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="7.658" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-51.69,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="5.9639311" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="18.00432" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="26.393833" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="30.557331" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="39.584499" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="46.273602" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="57.626328" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="61.789825" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="70.816994" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="77.693642" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,30.17,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,35.04,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> </text> </g> </g> </svg>和<年代vg height="17.137501" id="M188" style="vertical-align:-2.53308pt;width:141.41251px;" version="1.1" viewbox="0 0 141.41251 17.137501" width="141.41251" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.1375)"> <g transform="translate(72,-58.29)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5006001" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-60.88,65.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="7.658" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-49.81,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="5.9639311" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="18.00432" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="26.393833" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="30.557331" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="39.584499" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="46.273602" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="57.613823" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="61.777325" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="70.804489" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="77.681137" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,32.04,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,36.92,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> </text> </g> </g> </svg>,我们发现<年代pan class="equation" id="EEq28"> <svg height="19.700001" id="M189" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.700001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.7)"> <g transform="translate(72,-56.24)"> <text transform="matrix(1,0,0,-1,141.04,62.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.49"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5" y="1.75"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,150.23,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.128336" y="0"> +</t年代pan> <tspan style="font-size: 8.75px; " x="15.123456" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="19.499456" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,173.14,62.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.49"> |</t年代pan> <tspan style="font-size: 12.50px; " x="29.49" y="4.27"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.98" y="1.75"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="18.007887" y="1.75"> </t年代pan> <tspan style="font-size: 12.50px; " x="35.34" y="1.75"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="44.367165" y="1.75"> </t年代pan> <tspan style="font-size: 12.50px; " x="51.056271" y="1.75"> +</t年代pan> <tspan style="font-size: 12.50px; " x="62.396492" y="1.75"> (</t年代pan> <tspan style="font-size: 12.50px; " x="66.55999" y="1.75"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="75.587158" y="1.75"> </t年代pan> <tspan style="font-size: 12.50px; " x="82.463806" y="1.75"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,259.77,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,264.65,58.34)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.9299998" y="-2.52"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="200.10001" y="-2.6600001"> (</t年代pan> <tspan style="font-size: 12.50px; " x="204.2635" y="-2.6600001"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="210.515" y="-2.6600001"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="213.64075" y="-2.6600001"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="219.89224" y="-2.6600001"> )</t年代pan> </text> </g> </g> </svg></span>因此subdiffusive模式的振幅趋于零时空网趋于零。采用帕关系,这意味着错误的规范<年代vg height="25.6625" id="M190" style="vertical-align:-5.84473pt;width:197.8125px;" version="1.1" viewbox="0 0 197.8125 25.6625" width="197.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,25.6625)"> <g transform="translate(72,-51.47)"> <text transform="matrix(1,0,0,-1,-71.95,57.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 为</t年代pan> <tspan style="font-size: 12.50px; " x="6.5390692" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-59.85,62.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="7.658" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,-48.78,57.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 为</t年代pan> </text> <text transform="matrix(1,0,0,-1,-42.24,64.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-33.89,57.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≡</t年代pan> <tspan style="font-size: 12.50px; " x="14.12" y="0.029999999"> ∑</t年代pan> </text> <text transform="matrix(1,0,0,-1,-8.34,53.65)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-1.83,57.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5006001" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,6.24,63.4)"> <tspan style="font-size: 8.75px; " x="0" y="10.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="7.658" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,17.31,57.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> </text> <text transform="matrix(1,0,0,-1,19.81,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,28.15,57.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="0.029999999"> ∑</t年代pan> </text> <text transform="matrix(1,0,0,-1,51.62,53.65)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,58.56,57.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5006001" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,67.75,63.4)"> <tspan style="font-size: 8.75px; " x="0" y="8.71"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="7.658" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,78.82,57.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> </text> <text transform="matrix(1,0,0,-1,81.32,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>为0时<年代vg height="10.8" id="M191" 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pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代pan> </text> </g> </g> </svg>和<年代vg height="10.8" id="M192" style="vertical-align:-0.11285pt;width:20px;" version="1.1" viewbox="0 0 20 10.8" width="20" 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pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代pan> </text> </g> </g> </svg>去零。这是我们旨在证明。</gydF4y2Bap> <h4 id="conclusions">6。结论</gydF4y2Bah4> <p>显式方法求解分数阶扩散方程,涉及到几个分数Riemann-Liouville衍生品,通过Grunwald-Letnikov公式近似,被认为是。该方法用于解决一类这种类型的方程(部分电缆方程)和自由边界条件,狄拉克δ初始条件,不同的分级指数。数值方法的误差兼容删除错误,订单<年代vg height="16.75" id="M193" style="vertical-align:-2.21957pt;width:103.625px;" version="1.1" viewbox="0 0 103.625 16.75" width="103.625" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.1521959" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="13.315695" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="22.342861" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="26.2563" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="33.195465" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="44.535686" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="53.687881" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="57.851379" y="0"> Δ</t年代pan> <tspan style="font-size: 12.50px; " x="66.878548" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="73.755196" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,5.97,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>。它也证明了方法的收敛。除此之外,它也发现,部分冯·诺依曼稳定性分析,提供非常精确的稳定条件标准分级扩散方程,还导致一个非常准确的估计为电缆方程的稳定性条件。</gydF4y2Bap> </div> </div> <div class="ArticleReferences_xmlContent__p_40j"> <h4 class="ArticleReferences_references__GH2t_" id="references">引用</gydF4y2Bah4> <ol class="ArticleReferences_orderedReferences__mJr9M"> <li class="ArticleReferences_articleReference__ouEuh" id="B1"> <div class="referenceContent"> <p class="referenceText">r . 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