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用改进的欧拉方法求解初值问题,其中一阶微分方程未y f(x,y)
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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/627050b57b370112142f5990/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/627050b57b370112142f5990/bg1.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x1 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">/****************************************************************</div><div class="t m0 x1 h3 y3 ff1 fs0 fc0 sc0 ls0 ws0">******** </div><div class="t m0 x1 h4 y4 ff1 fs0 fc0 sc0 ls0 ws0">* <span class="ff2">&#29992;&#25913;&#36827;&#30340;&#27431;&#25289;&#26041;&#27861;&#27714;&#35299;&#21021;&#20540;&#38382;&#39064;&#65292;&#20854;&#20013;&#19968;&#38454;&#24494;&#20998;&#26041;&#31243;&#26410;<span class="_ _0"> </span></span>y'=f(x,y) </div><div class="t m0 x1 h4 y5 ff1 fs0 fc0 sc0 ls0 ws0">* <span class="ff2">&#21021;&#22987;&#26465;&#20214;&#20026;<span class="_ _0"> </span></span>x=x[0]<span class="ff2">&#26102;</span>,y<span class="ff2">&#65309;</span>y[0]. </div><div class="t m0 x1 h4 y6 ff1 fs0 fc0 sc0 ls0 ws0">* <span class="ff2">&#36755;&#20837;</span>: f--<span class="ff2">&#20989;&#25968;<span class="_ _0"> </span></span>f(x,y)<span class="ff2">&#30340;&#25351;&#38024;</span> </div><div class="t m0 x1 h4 y7 ff1 fs0 fc0 sc0 ls0 ws0">* &#58898;&#58898;&#58898;&#58898;&#58898;&#58898;x--<span class="ff2">&#33258;&#21464;&#37327;&#31163;&#25955;&#20540;&#25968;&#32452;</span>(<span class="ff2">&#20854;&#20013;<span class="_ _0"> </span></span>x[0]<span class="ff2">&#20026;&#21021;&#22987;&#26465;&#20214;</span>) </div><div class="t m0 x1 h4 y8 ff1 fs0 fc0 sc0 ls0 ws0">* &#58898;&#58898;&#58898;&#58898;&#58898;&#58898;y--<span class="ff2">&#23545;&#24212;&#20110;&#33258;&#21464;&#37327;&#31163;&#25955;&#20540;&#30340;&#20989;&#25968;&#20540;&#25968;&#32452;</span>(<span class="ff2">&#20854;&#20013;<span class="_ _0"> </span></span>y[0]<span class="ff2">&#20026;&#21021;&#22987;&#26465;&#20214;</span>) </div><div class="t m0 x1 h4 y9 ff1 fs0 fc0 sc0 ls0 ws0">* &#58898;&#58898;&#58898;&#58898;&#58898;&#58898;h--<span class="ff2">&#35745;&#31639;&#27493;&#38271;</span> </div><div class="t m0 x1 h4 ya ff1 fs0 fc0 sc0 ls0 ws0">* &#58898;&#58898;&#58898;&#58898;&#58898;&#58898;n--<span class="ff2">&#27493;&#25968;</span> </div><div class="t m0 x1 h4 yb ff1 fs0 fc0 sc0 ls0 ws0">* <span class="ff2">&#36755;&#20986;</span>: x<span class="_ _0"> </span><span class="ff2">&#20026;&#35828;&#27714;&#35299;&#30340;&#33258;&#21464;&#37327;&#31163;&#25955;&#20540;&#25968;&#32452;</span> </div><div class="t m0 x1 h4 yc ff1 fs0 fc0 sc0 ls0 ws0">* &#58898;&#58898;&#58898;&#58898;&#58898;&#58898;y<span class="_ _0"> </span><span class="ff2">&#20026;&#25152;&#27714;&#35299;&#23545;&#24212;&#20110;&#33258;&#21464;&#37327;&#31163;&#25955;&#20540;&#30340;&#20989;&#25968;&#20540;&#25968;&#32452;</span> </div><div class="t m0 x1 h3 yd ff1 fs0 fc0 sc0 ls0 ws0">*****************************************************************</div><div class="t m0 x1 h3 ye ff1 fs0 fc0 sc0 ls0 ws0">*******/ </div><div class="t m0 x1 h3 yf ff1 fs0 fc0 sc0 ls0 ws0">double proved_euler(double(*f)(double,double),double x[], </div><div class="t m0 x1 h3 y10 ff1 fs0 fc0 sc0 ls0 ws0">double y[],double h,int n) </div><div class="t m0 x1 h3 y11 ff1 fs0 fc0 sc0 ls0 ws0">{ </div><div class="t m0 x1 h3 y12 ff1 fs0 fc0 sc0 ls0 ws0">int i; </div><div class="t m0 x1 h3 y13 ff1 fs0 fc0 sc0 ls0 ws0">double xs,ys,yp; </div><div class="t m0 x1 h3 y14 ff1 fs0 fc0 sc0 ls0 ws0">for(i=0;i&lt;n;i++) </div><div class="t m0 x1 h3 y15 ff1 fs0 fc0 sc0 ls0 ws0">{ </div><div class="t m0 x1 h3 y16 ff1 fs0 fc0 sc0 ls0 ws0">ys=y<span class="ff3">; </span></div><div class="t m0 x1 h3 y17 ff3 fs0 fc0 sc0 ls0 ws0">xs=x; </div><div class="t m0 x1 h3 y18 ff3 fs0 fc0 sc0 ls0 ws0">y[i+1]=y; </div><div class="t m0 x1 h3 y19 ff3 fs0 fc0 sc0 ls0 ws0">yp=(*f)(xs,ys); //k1 </div><div class="t m0 x1 h3 y1a ff3 fs0 fc0 sc0 ls0 ws0">y[i+1]+=yp*h/2.0; </div><div class="t m0 x1 h3 y1b ff3 fs0 fc0 sc0 ls0 ws0">ys+=h*yp; </div><div class="t m0 x1 h3 y1c ff3 fs0 fc0 sc0 ls0 ws0">xs+=h; </div><div class="t m0 x1 h3 y1d ff3 fs0 fc0 sc0 ls0 ws0">yp=(*f)(xs,ys); //k2 </div><div class="t m0 x1 h3 y1e ff3 fs0 fc0 sc0 ls0 ws0">y[i+1]+=yp*h/2.0; </div><div class="t m0 x1 h3 y1f ff3 fs0 fc0 sc0 ls0 ws0">x[i+1]=xs; </div><div class="t m0 x1 h3 y20 ff3 fs0 fc0 sc0 ls0 ws0">} </div><div class="t m0 x1 h3 y21 ff3 fs0 fc0 sc0 ls0 ws0">return(0); </div><div class="t m0 x1 h3 y22 ff3 fs0 fc0 sc0 ls0 ws0">}</div></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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