求解Bessel方程.rar

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使用差分法解一类Bessel方程在不同边界条件下的离散解
求解Bessel方程.rar
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<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/626c59647ae5df2aa730c6d0/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/626c59647ae5df2aa730c6d0/bg1.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x1 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">&#19968;&#31867;<span class="_ _0"> </span><span class="ff2 sc1">Bessel<span class="_ _0"> </span></span>&#26041;&#31243;&#22312;&#19981;&#21516;&#36793;&#30028;&#26465;&#20214;&#19979;&#30340;&#24046;&#20998;&#35299;</div><div class="t m0 x2 h4 y3 ff2 fs1 fc0 sc1 ls0 ws0"> <span class="ff1">&#20449;&#24687;&#19982;&#35745;&#31639;&#26426;&#31185;&#23398;&#19987;&#19994; &#36213;&#37995;</span></div><div class="t m0 x3 h4 y4 ff1 fs1 fc0 sc1 ls0 ws0">&#25351;&#23548;&#32769;&#24072;&#65306;&#26446;&#39034;&#21021; &#25945;&#25480;</div><div class="t m0 x3 h5 y5 ff3 fs1 fc0 sc1 ls0 ws0"> </div><div class="t m0 x4 h4 y6 ff1 fs1 fc0 sc1 ls0 ws0">&#12304;&#25688;&#35201;&#12305;<span class="_ _1"></span> &#26412;&#25991;&#20027;<span class="_ _1"></span>&#35201;&#38416;&#36848;&#30340;&#26159;&#20351;&#29992;&#24046;<span class="_ _1"></span>&#20998;&#27861;&#35299;&#19968;&#31867;<span class="_ _2"> </span><span class="ff3">Bessel<span class="_ _3"> </span></span>&#26041;&#31243;&#22312;&#19981;&#21516;<span class="_ _1"></span>&#36793;&#30028;&#26465;&#20214;&#19979;&#30340;<span class="_ _1"></span>&#31163;&#25955;&#35299;&#65292;&#20197;&#21450;<span class="_ _1"></span>&#20351;&#29992;&#36861;&#36214;&#27861;&#27714;</div><div class="t m0 x4 h4 y7 ff1 fs1 fc0 sc1 ls0 ws0">&#35299;&#24471;&#21040;<span class="_ _1"></span>&#30340;&#32447;&#24615;<span class="_ _1"></span>&#26041;&#31243;&#32452;<span class="_ _1"></span><span class="ff3">.<span class="_ _1"></span></span>&#22312;&#24471;&#21040;<span class="_ _1"></span>&#26041;&#31243;&#30340;<span class="_ _1"></span>&#31163;&#25955;&#35299;<span class="_ _1"></span>&#21518;&#65292;<span class="_ _1"></span>&#21033;&#29992;<span class="_ _4"> </span><span class="ff3">MA<span class="_ _5"></span>TLAB<span class="_ _3"> </span><span class="ff1">&#31243;<span class="_ _1"></span>&#24207;&#65292;&#32472;<span class="_ _1"></span>&#21046;&#26041;&#31243;<span class="_ _1"></span>&#30340;&#31163;&#25955;<span class="_ _1"></span>&#35299;&#65292;&#24182;<span class="_ _6"></span>&#20998;&#26512;&#36825;<span class="_ _1"></span>&#20123;&#31163;&#25955;<span class="_ _1"></span>&#35299;</span></span></div><div class="t m0 x4 h4 y8 ff1 fs1 fc0 sc1 ls0 ws0">&#26500;&#25104;&#30340;&#35299;&#26354;&#32447;&#65292;&#21450;&#21508;&#31181;&#21442;&#25968;&#30340;&#21464;&#21270;&#23545;&#35299;&#26354;&#32447;&#30340;&#24433;&#21709;&#12290;</div><div class="t m0 x4 h4 y9 ff1 fs1 fc0 sc1 ls0 ws0">&#20851;&#38190;&#23383;&#65306;&#24494;&#20998;&#26041;&#31243; <span class="ff3">Bessel<span class="_ _3"> </span></span>&#26041;&#31243; &#24046;&#20998;&#27861; <span class="ff3">MA<span class="_ _5"></span>TLAB<span class="_ _3"> </span><span class="ff1">&#31243;&#24207; </span></span></div><div class="t m0 x5 h6 ya ff4 fs1 fc0 sc1 ls0 ws0">The kind of Bessel equation dissolve in differ<span class="_ _7"></span>ent boundary</div><div class="t m0 x4 h4 yb ff1 fs1 fc0 sc1 ls0 ws0">&#12304;<span class="_ _8"> </span><span class="ff5">Abstract<span class="_ _8"> </span></span>&#12305;<span class="_ _8"> </span><span class="ff5"> <span class="_ _8"> </span> <span class="_ _8"> </span>This<span class="_ _6"></span> <span class="_ _6"></span>thesis <span class="_ _8"> </span>introduces<span class="_ _6"></span> <span class="_ _8"> </span> <span class="_ _6"></span>solving<span class="_ _6"></span> <span class="_ _6"></span>the<span class="_ _8"> </span> <span class="_ _1"></span><span class="fc1">kind<span class="_ _8"> </span> </span>of<span class="_ _6"></span> <span class="_ _8"> </span> <span class="_ _6"></span>Bessel<span class="_ _6"></span> <span class="_ _9"></span>equation<span class="_ _6"></span> <span class="_ _3"> </span> in<span class="_ _6"></span> <span class="_ _9"></span>different<span class="_ _6"></span> <span class="_ _6"></span>boundary<span class="_ _6"></span> <span class="_ _8"> </span> <span class="_ _6"></span>by<span class="_ _6"></span> <span class="_ _6"></span>d<span class="_ _1"></span>iffer<span class="_ _7"></span>ence</span></div><div class="t m0 x4 h6 yc ff5 fs1 fc0 sc1 ls0 ws0">method and gains discrete<span class="_ _1"></span> solution, and solving the linear equation by <span class="_ _1"></span><span class="fc1">chase </span>method . Protracting the <span class="_ _1"></span>discrete solution</div><div class="t m0 x4 h6 yd ff5 fs1 fc0 sc1 ls0 ws0">of<span class="_ _1"></span> <span class="_ _1"></span>the<span class="_ _6"></span> Bessel<span class="_ _1"></span> <span class="_ _1"></span>equation<span class="_ _1"></span> <span class="_ _1"></span>by<span class="_ _1"></span> <span class="_ _1"></span>Matlab,<span class="_ _1"></span> <span class="_ _1"></span>and <span class="_ _6"></span>observing <span class="_ _1"></span>the<span class="_ _1"></span> <span class="_ _6"></span>curve <span class="_ _1"></span>which<span class="_ _1"></span> <span class="_ _1"></span>is<span class="_ _1"></span> <span class="_ _1"></span>compose<span class="_ _1"></span> <span class="_ _1"></span>of<span class="_ _1"></span> <span class="_ _1"></span>the<span class="_ _6"></span> <span class="_ _6"></span>discrete <span class="_ _6"></span>solution,<span class="_ _6"></span> discussing <span class="_ _6"></span>the</div><div class="t m0 x4 h6 ye ff5 fs1 fc0 sc1 ls0 ws0">condition of the curve in different param<span class="_ _7"></span>eter<span class="_ _5"></span>.<span class="_ _1"></span> </div><div class="t m0 x4 h6 yf ff5 fs1 fc0 sc1 ls0 ws0"> Key word: Bessel function Matlab program Diff<span class="_ _7"></span>erence method</div><div class="t m0 x4 h3 y10 ff1 fs0 fc0 sc0 ls0 ws0">&#19968; &#21069;&#35328;</div><div class="t m0 x6 h4 y11 ff3 fs1 fc0 sc1 ls0 ws0">Bessel<span class="_ _3"> </span><span class="ff1">&#20989;&#25968;&#26159;&#24037;&#31243;<span class="_ _1"></span>&#25216;&#26415;&#20013;&#24120;&#29992;&#30340;<span class="_ _1"></span>&#19968;&#31181;&#29305;&#27530;&#20989;&#25968;<span class="_ _1"></span>&#65292;&#20027;&#35201;&#22320;&#26469;&#28304;<span class="_ _1"></span>&#20110;&#22278;&#26609;&#24418;&#25110;&#22278;&#26609;&#29289;<span class="_ _1"></span>&#20307;&#30340;&#26377;&#20851;&#29289;&#29702;<span class="_ _1"></span>&#38382;&#39064;&#65292;&#22240;</span></div><div class="t m0 x4 h4 y12 ff1 fs1 fc0 sc1 ls0 ws0">&#27492;<span class="_ _a"> </span>&#20063;<span class="_ _a"> </span>&#21483;<span class="_ _a"> </span>&#20570;<span class="_ _a"> </span>&#22278;<span class="_ _a"> </span>&#26609;<span class="_ _b"> </span>&#20989;<span class="_ _a"> </span>&#25968;<span class="_ _b"> </span>&#12290;<span class="_ _a"> </span>&#36825;<span class="_ _a"> </span>&#31181;<span class="_ _a"> </span>&#20989;<span class="_ _a"> </span>&#25968;<span class="_ _a"> </span>&#26159;<span class="_ _b"> </span>&#30740;<span class="_ _a"> </span>&#31350;<span class="_ _c"> </span>&#19968;<span class="_ _a"> </span>&#20123;<span class="_ _a"> </span>&#29289;<span class="_ _b"> </span>&#29702;<span class="_ _a"> </span>&#38382;<span class="_ _a"> </span>&#39064;<span class="_ _a"> </span>&#26102;<span class="_ _a"> </span>&#25152;<span class="_ _a"> </span>&#24402;<span class="_ _b"> </span>&#32467;<span class="_ _a"> </span>&#25104;<span class="_ _a"> </span>&#30340;<span class="_ _a"> </span>&#36125;<span class="_ _a"> </span>&#22622;<span class="_ _a"> </span>&#23572;<span class="_ _b"> </span>&#26041;<span class="_ _a"> </span>&#31243;</div><div class="t m0 x7 h4 y13 ff1 fs1 fc0 sc1 ls0 ws0">&#30340;&#35299;&#12290;</div><div class="t m0 x8 h4 y14 ff1 fs1 fc0 sc1 ls0 ws0">&#26089;&#22312;&#36125;<span class="_ _1"></span>&#22622;&#23572;&#20043;<span class="_ _1"></span>&#21069;&#65292;&#27431;<span class="_ _1"></span>&#25289;&#65288;<span class="_ _1"></span><span class="ff3">Eule<span class="_ _1"></span>r</span>&#65289;&#12289;<span class="_ _1"></span>&#25289;&#26684;&#26391;<span class="_ _1"></span>&#26085;&#65288;<span class="_ _c"> </span><span class="ff3">Lagrange<span class="_ _1"></span></span>&#65289;&#31561;<span class="_ _1"></span>&#20154;&#30740;&#31350;<span class="_ _1"></span>&#36807;&#36825;&#20010;<span class="_ _1"></span>&#26041;&#31243;&#65292;<span class="_ _1"></span>&#24182;&#27714;&#20986;<span class="_ _1"></span>&#20102;&#23427;&#30340;&#36890;<span class="_ _1"></span>&#35299;<span class="_ _6"></span>&#12290;</div><div class="t m0 x4 h4 y15 ff1 fs1 fc0 sc1 ls0 ws0">&#36125;&#22622;&#23572;&#22312;<span class="_ _3"> </span><span class="ff3">1824<span class="_ _4"> </span></span>&#24180;&#20851;&#20110;&#22825;&#25991;&#23398;<span class="_ _1"></span>&#38382;&#39064;&#30340;&#30740;&#31350;&#20013;<span class="_ _1"></span>&#65292;&#31995;&#32479;&#22320;&#30740;&#31350;<span class="_ _1"></span>&#20102;&#27492;&#26041;&#31243;&#30340;&#35299;<span class="_ _1"></span>&#65292;&#21516;&#26102;&#32534;&#21046;&#20986;<span class="_ _1"></span>&#36825;&#20123;&#20989;&#25968;&#20855;&#26377;&#21313;&#20301;<span class="_ _1"></span>&#23567;&#25968;</div><div class="t m0 x4 h4 y16 ff1 fs1 fc0 sc1 ls0 ws0">&#30340;&#20989;&#25968;&#34920;&#12290;&#27492;&#21518;&#65292;&#31216;&#36825;&#31181;&#20989;&#25968;&#20026;&#36125;&#22622;&#23572;&#20989;&#25968;&#65292;&#24182;&#34987;&#24191;&#27867;&#22320;&#24212;&#29992;&#21040;&#29289;&#29702;&#23398;&#21644;&#25216;&#26415;&#31185;&#23398;&#20013;&#12290;</div><div class="t m0 x8 h4 y17 ff1 fs1 fc0 sc1 ls0 ws0">&#26412;<span class="_ _6"></span>&#25991;<span class="_ _6"></span>&#20027;<span class="_ _6"></span>&#35201;<span class="_ _6"></span>&#38416;<span class="_ _9"></span>&#36848;<span class="_ _6"></span>&#30340;<span class="_ _6"></span>&#26159;<span class="_ _6"></span>&#20351;<span class="_ _6"></span>&#29992;<span class="_ _9"></span>&#24046;<span class="_ _6"></span>&#20998;<span class="_ _6"></span>&#27861;<span class="_ _6"></span>&#35299;<span class="_ _6"></span>&#19968;<span class="_ _9"></span>&#31867;<span class="_"> </span><span class="ff3">B<span class="_ _7"></span>essel<span class="_ _2"> </span><span class="ff1">&#26041;<span class="_ _6"></span>&#31243;<span class="_ _6"></span>&#22312;<span class="_ _6"></span>&#19981;<span class="_ _9"></span>&#21516;<span class="_ _6"></span>&#36793;<span class="_ _6"></span>&#30028;<span class="_ _6"></span>&#26465;<span class="_ _6"></span>&#20214;<span class="_ _6"></span>&#19979;<span class="_ _9"></span>&#30340;<span class="_ _6"></span>&#23450;<span class="_ _6"></span>&#35299;<span class="_ _6"></span>&#38382;<span class="_ _6"></span>&#39064;<span class="_ _9"></span>&#30340;<span class="_ _6"></span>&#31163;<span class="_ _6"></span>&#25955;<span class="_ _6"></span>&#35299;<span class="_ _6"></span>&#65292;<span class="_ _9"></span>&#24182;<span class="_ _6"></span>&#20511;<span class="_ _6"></span>&#21161;</span></span></div><div class="t m0 x4 h4 y18 ff3 fs1 fc0 sc1 ls0 ws0">MA<span class="_ _5"></span>TLAB<span class="_ _3"> </span><span class="ff1">&#31243;&#24207;&#30340;&#32472;&#22270;&#24037;&#20855;&#23545;&#20854;&#32473;&#20104;&#30452;&#35266;&#30340;&#34920;&#29616;&#65292;&#20998;&#26512;&#22312;&#19981;&#21516;&#36793;&#30028;&#26465;&#20214;&#19979;&#21442;&#25968;&#30340;&#21464;&#21270;&#23545;&#35299;&#26354;&#32447;&#30340;&#24433;&#21709;&#12290;</span></div><div class="t m0 x4 h3 y19 ff1 fs0 fc0 sc0 ls0 ws0">&#20108; &#20989;&#25968;&#27169;&#22411;&#21450;&#20854;&#27714;&#35299;</div><div class="t m0 x4 h4 y1a ff3 fs1 fc0 sc1 ls0 ws0">2.1 <span class="ff1">&#27169;&#22411;&#30340;&#24314;&#31435;</span></div><div class="t m0 x8 h4 y1b ff1 fs1 fc0 sc1 ls0 ws0">&#26412;&#25991;&#35201;&#27714;&#35299;&#30340;&#27169;&#22411;&#22914;&#19979;&#65306;</div><div class="t m0 x4 h4 y1c ff3 fs1 fc0 sc1 ls0 ws0">2.2 <span class="ff1">&#27169;&#22411;&#30340;&#20998;&#26512;&#19982;&#27714;&#35299;</span></div><div class="t m0 x9 h4 y1d ff1 fs1 fc0 sc1 ls0 ws0">&#37319;&#29992;&#24046;&#20998;&#27861;&#27714;&#35299;&#19978;&#38754;&#30340;&#27169;&#22411;&#65292;&#39318;&#20808;&#24212;&#35813;&#21033;&#29992;&#23548;&#25968;&#30340;&#23450;&#20041;&#23558;&#23548;&#25968;&#21270;&#20026;&#65306;</div><div class="t m0 xa h5 y1e ff3 fs1 fc0 sc1 ls0 ws0"> (1)</div></div><div class="t m0 xb h7 y1f ff5 fs2 fc0 sc1 ls0 ws0">1</div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div> </body> </html>
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