API tools faq
paste
Advertisement
enkov

Nonlinear Hammerstein fuzzy functional integral equations

enkov
May 28th, 2017
626
0
Never
Add comment
Not a member of Pastebin yet? Sign Up, it unlocks many cool features!
JavaScript 20.94 KB | None | 0 0
raw download clone embed print report
  1. <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
  2. "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
  3. <html>
  4.     <title>Web-based solver example</title>
  5.     <meta name="Description" content="Web-based nonlinear Hammerstein fuzzy functional integral equations solver" />
  6.     <meta name="Keywords" content="fuzzy integral equation, Hammerstein, solver, numerical method, approximate method" />
  7.     <meta name="Author" content="Svetoslav Enkov. Atanaska Georgieva, Renato Nikolla" />
  8.     <meta charset="UTF-8" />
  9. <head>
  10.    <link href="solver.css" type="text/css" rel="stylesheet">
  11. </head>
  12. <body>
  13. <p align="center" style="font-size: 150%">Solver for nonlinear Hammerstein fuzzy
  14. functional integral equations</p>
  15.  
  16. <form name="EvalForm" id="EvalCalc" action="" method="post" novalidate="novalidate" scrolling="yes">
  17.  
  18. <div id="Formulaes">
  19. <p>&nbsp;&nbsp;g<sub>-</sub>(t,r) = <input name="glfunc" value="" type="text" size=115></p>
  20. <p>&nbsp;&nbsp;g<sub>+</sub>(t,r) = <input name="gufunc" value="" type="text" size=115></p>
  21. <p>&nbsp;&nbsp;&nbsp;k(t,s) = <input name="kfunc" value="" type="text" size=115></p>
  22. <p>H<sub>-</sub>(t,x,r) = <input name="Hlfunc" value="" type="text" size=115></p>
  23. <p>H<sub>+</sub>(t,x,r) = <input name="Hufunc" value="" type="text" size=115></p>
  24. <p>f<sub>-</sub>(t,x,r) = <input name="flfunc" value="" type="text" size=115></p>
  25. <p>f<sub>+</sub>(t,x,r) = <input name="fufunc" value="" type="text" size=115></p>
  26. <p>&nbsp;x*<sub>-</sub>(t,r) = <input name="xlfunc" value="" type="text" size=115></p>
  27. <p>&nbsp;x*<sub>+</sub>(t,r) = <input name="xufunc" value="" type="text" size=115></p>
  28. <p>
  29. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
  30.  a = <input name="avalue" value="" type="text" size=6> &nbsp;
  31.  b = <input name="bvalue" value="" type="text" size=6> &nbsp;&nbsp;
  32.  &epsilon;' = <input name="epsvalue" value="" type="text" size=10> &nbsp;
  33.  n = <input name="nvalue" value="" type="text" size=4> &nbsp;
  34.  r = <input name="rvalue" value="" type="text" size=6> &nbsp;
  35. </p>
  36. </div>
  37.  
  38. <p><span align='left'>&nbsp;&nbsp;<input name = "CalcButton" value="Calculate" type="button" title="Evaluates the expression!" onclick="StartCalc();">&nbsp;&nbsp;&nbsp;<span id="ErrorLabel">
  39. </span>
  40. <p align='right'>
  41. <input name = "SampleButton" value="Load sample" type="button" title="Loads Sample!" onclick="Sample();">&nbsp;&nbsp;&nbsp;
  42. <input name = "PlotButton" value="Plot results" type="button" title="Plot of the results!" onclick="PlotGraph();">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</p>
  43.  
  44. <div  id="animated-result" class="animated fadeInLeft" align="center" style="display:none">
  45. <span id="ResultLabel1"></span><br>
  46. <span id="ResultLabel2"></span>
  47. <table id="ResultsErrors" class="ResultTable"></table><br>
  48. <table id="ResultsValues" class="ResultTable"></table><br>
  49. </div>
  50.  
  51. <div style='font-family: "Times New Roman", Times, serif;'>Note: use E instead of e, PI instead of &pi;, ^ for power, etc...</div>
  52.  
  53. <div align="center" class="center-block">
  54. <br><span id="resultsplot"></span>
  55. <br><span id="plotlegend" style="display:none; font-size: 75%">
  56. Colors: Red - upper optimal, Blue - lower optimal, Black - upper exact, Brown - lower exact, Magenta - upper trapezoid, Pink - lower trapezoid.<br>Use zoom with mouse wheel to see in detail.
  57. </span>
  58. </div>
  59.  
  60. <div><a href=
  61. "Numerical%20Solution%20of%20Nonlinear%20Hammerstein%20Fuzzy%20Functional%20Integral%20Equations%20-%20Enkov%20Georgieva%20Nikolla.pdf" target="_blank"><img src="pdf-download-icon.png" alt="Read entire article in PDF" style="width:291px;height:92px;border:0;">
  62. </a>
  63. </div>
  64.  
  65. </form>
  66.  
  67. <script src="lib/parser.js" type="text/javascript"></script>
  68. <script src="https://d3js.org/d3.v3.min.js" charset="utf-8"></script>
  69. <script src="https://wzrd.in/standalone/function-plot@1.17.0"></script>
  70.  
  71. <script type="text/javascript">
  72. // Copyright (c)2015 Matthew Crumley, Math Parser library, https://silentmatt.com/javascript-expression-evaluator/
  73. //  - please use old version, not new ECMAScript 6 version
  74. // Copyright (c)2016 Maurizio Poppe, Function Plot plotting library, http://maurizzzio.github.io/function-plot/ 1.17.0
  75. //
  76. // Copyright (c)2016 Algorithm realisation by Svetoslav Enkov, Atanaska Georgieva, Renato Nikolla, freeware, public domain
  77. // University of Plovdiv, FMI, 236 Bulgaria Blvd., Plovdiv, Bulgaria. enkov@uni-plovdiv.bg
  78. // published at http://enkov.com/solver
  79. // https://pastebin.com/aTR7rYZ8
  80. //
  81. // Algorithm is based on the presentation at APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE’16): Proceedings of the 42nd International Conference on Applications of Mathematics in Engineering and Economics
  82. // article "Numerical solution of nonlinear Hammerstein fuzzy functional integral equations", DOI 10.1063/1.4968452
  83.  
  84. var d3 = window.d3;
  85. var functionPlot = window.functionPlot;
  86. var sFormElements = document.forms["EvalForm"].elements;
  87. var Calculated = false;
  88. // forward definitions (global) to be seen in the plotting function too
  89. var n; var m; var mo; var t; var to;
  90. var xml; var xmu; var xoml; var xomu; var xl; var xu;
  91. var a; var b;
  92.  
  93. function PlotGraph()
  94. {
  95.     if (!Calculated) {
  96.         alert("You haven't calculated nothing yet!");
  97.         return;
  98.     }
  99.     document.getElementById('plotlegend').style.display = ''; // show the legend
  100.     var pointsTL = [];
  101.     var pointsEL = [];
  102.     var pointsOL = [];
  103.     var pointsTU = [];
  104.     var pointsEU = [];
  105.     var pointsOU = [];
  106.     var minY = xml[m][0];
  107.     var maxY = xml[m][0];
  108.     for (var i=0; i<=n; i++) {
  109.         pointsTL.push([t[i],xml[m][i]]); // trapezoid
  110.         minY = Math.min(minY, xml[m][i]);
  111.         maxY = Math.max(maxY, xml[m][i]);      
  112.         pointsEL.push([t[i],xl[i]]); // exact
  113.         minY = Math.min(minY, xl[i]);
  114.         maxY = Math.max(maxY, xl[i]);      
  115.         if (i > 0) {
  116.             pointsOL.push([t[i],xoml[mo][i]]);   // optimal
  117.             minY = Math.min(minY, xoml[mo][i]);
  118.             maxY = Math.max(maxY, xoml[mo][i]);
  119.         }
  120.         pointsTU.push([t[i],xmu[m][i]]); // trapezoid
  121.         minY = Math.min(minY, xmu[m][i]);
  122.         maxY = Math.max(maxY, xmu[m][i]);      
  123.         pointsEU.push([t[i],xu[i]]); // exact
  124.         minY = Math.min(minY, xu[i]);
  125.         maxY = Math.max(maxY, xu[i]);      
  126.         if (i > 0) {
  127.             pointsOU.push([t[i],xomu[mo][i]]);  // optimal
  128.             minY = Math.min(minY, xomu[mo][i]);
  129.             maxY = Math.max(maxY, xomu[mo][i]);
  130.         }
  131.     }
  132.     // plot the results
  133.     functionPlot({
  134.         title: 'Graphics (drag and zoom with mouse)',
  135.         target: '#resultsplot',
  136.           xAxis: {
  137.             domain: [a-Math.abs(b-a)*0.1, b+Math.abs(b-a)*0.1]
  138.         },
  139.           yAxis: {
  140.             domain: [minY-Math.abs(maxY-minY)*0.1, maxY+Math.abs(maxY-minY)*0.1]
  141.         },
  142.         data: [{
  143.             points: pointsEU,
  144.             fnType: 'points',
  145.             graphType: 'polyline',
  146.             color: 'black'
  147.         }, {
  148.             points: pointsTU,
  149.             fnType: 'points',
  150.             graphType: 'polyline',
  151.             color: 'magenta'
  152.         }, {
  153.             points: pointsOU,
  154.             fnType: 'points',
  155.             graphType: 'polyline',
  156.             color: 'red'
  157.         },{
  158.             points: pointsEL,
  159.             fnType: 'points',
  160.             graphType: 'polyline',
  161.             color: 'brown'
  162.         }, {
  163.             points: pointsTL,
  164.             fnType: 'points',
  165.             graphType: 'polyline',
  166.             color: 'pink'
  167.         }, {
  168.             points: pointsOL,
  169.             fnType: 'points',
  170.             graphType: 'polyline',
  171.             color: 'blue'
  172.         }]
  173.     });
  174. }
  175.  
  176. function Sample()
  177. {   sFormElements["glfunc"].value = '-t/12+(3*t/54)*(1-r)-(1-r)/8';
  178.     sFormElements["gufunc"].value = '-t/12-(3*t/54)*(1-r)+(1-r)/8';
  179.     sFormElements["kfunc"].value = 't*s/3';
  180.     sFormElements["Hlfunc"].value = 'x*x';
  181.     sFormElements["Hufunc"].value = 'x*x';
  182.     sFormElements["flfunc"].value = 'x/4-(t/216)*(1-r)*(1-r)-(t/54)*(1-r)+3*t/4';
  183.     sFormElements["fufunc"].value = 'x/4-(t/216)*(1-r)*(1-r)+(t/54)*(1-r)+3*t/4';
  184.     sFormElements["xlfunc"].value = 't-(1-r)/6';
  185.     sFormElements["xufunc"].value = 't+(1-r)/6';
  186.     sFormElements["avalue"].value = '0';
  187.     sFormElements["bvalue"].value = '1';
  188.     sFormElements["epsvalue"].value = '1e-15';
  189.     sFormElements["nvalue"].value = '10';
  190.     sFormElements["rvalue"].value = '0.5';
  191.     document.getElementById("ErrorLabel").textContent = 'Loaded article sample function...';
  192.     document.getElementById("ResultLabel1").innerHTML = '';
  193.     document.getElementById("ResultTable").innerHTML = '';
  194. }
  195.  
  196. function myFixed(p1, p2){
  197.     if (Math.trunc(p1)==p1)
  198.         { return p1; }
  199.     else
  200.         { return p1.toFixed(p2); }
  201. }
  202.  
  203. function StartCalc()
  204. {
  205.     document.getElementById("ErrorLabel").textContent = 'Calculating...';
  206.     document.getElementById('animated-result').style.display = 'none'; // hide result
  207.     window.setTimeout(Calc, 100);
  208. }
  209.  
  210. function Calc()
  211. {try {
  212.  
  213.     // Get the initial values from the user's input
  214.    
  215.     document.getElementById("ErrorLabel").textContent = ''; // clear error
  216.     document.getElementById('animated-result').style.display = 'none'; // hide result
  217.     Calculated = false;
  218.  
  219.     var glx = sFormElements['glfunc'].value;
  220.     var gux = sFormElements['gufunc'].value;
  221.     var kx  = sFormElements['kfunc'].value;
  222.     var Hlx = sFormElements['Hlfunc'].value;
  223.     var Hux = sFormElements['Hufunc'].value;
  224.     var flx = sFormElements['flfunc'].value;
  225.     var fux = sFormElements['fufunc'].value;
  226.     var xlx = sFormElements['xlfunc'].value;
  227.     var xux = sFormElements['xufunc'].value;
  228.    
  229.     if (glx == '') { document.getElementById("ErrorLabel").textContent = 'Function g- can not be empty!'; return; }
  230.     if (gux == '') { document.getElementById("ErrorLabel").textContent = 'Function g+ can not be empty!'; return; }
  231.     if (kx == '') { document.getElementById("ErrorLabel").textContent = 'Function k can not be empty!'; return; }
  232.     if (Hlx == '') { document.getElementById("ErrorLabel").textContent = 'Function H- can not be empty!'; return; }
  233.     if (Hux == '') { document.getElementById("ErrorLabel").textContent = 'Function H+ can not be empty!'; return; }
  234.     if (flx == '') { document.getElementById("ErrorLabel").textContent = 'Function f- can not be empty!'; return; }
  235.     if (fux == '') { document.getElementById("ErrorLabel").textContent = 'Function f+ can not be empty!'; return; }
  236.     if (xlx == '') { document.getElementById("ErrorLabel").textContent = 'Function x*- can not be empty!'; return; }
  237.     if (xux == '') { document.getElementById("ErrorLabel").textContent = 'Function x*+ can not be empty!'; return; }
  238.  
  239.     a = (sFormElements['avalue'].value != '') ? parseFloat(sFormElements['avalue'].value) : 0.0;
  240.     b = (sFormElements['bvalue'].value != '') ? parseFloat(sFormElements['bvalue'].value) : 0.0;
  241.     var eps = (sFormElements['epsvalue'].value != '') ? parseFloat(sFormElements['epsvalue'].value) : 0.0;
  242.     n = (sFormElements['nvalue'].value != '') ? parseInt(sFormElements['nvalue'].value) : 0;
  243.     var r = (sFormElements['rvalue'].value != '') ? parseFloat(sFormElements['rvalue'].value) : 0.0;
  244.    
  245.     if (isNaN(a)) { document.getElementById("ErrorLabel").textContent = 'a value error!'; return; }
  246.     if (isNaN(b)) { document.getElementById("ErrorLabel").textContent = 'b value error!'; return; }
  247.     if (isNaN(eps)) { document.getElementById("ErrorLabel").textContent = 'eps value error!'; return; }
  248.     if (isNaN(n)) { document.getElementById("ErrorLabel").textContent = 'n value error!'; return; }
  249.     if (isNaN(r)) { document.getElementById("ErrorLabel").textContent = 'r value error!'; return; }
  250.    
  251.     if ( a >= b) { document.getElementById("ErrorLabel").textContent = 'a is not less than b error!'; return; }
  252.     if ( eps <= 0) { document.getElementById("ErrorLabel").textContent = 'eps must be greater than 0 error!'; return; }
  253.     if ( n <= 2) { document.getElementById("ErrorLabel").textContent = 'n must be greater than 2 error!'; return; }
  254.     if ( r < 0 || r > 1) { document.getElementById("ErrorLabel").textContent = 'r must be between 0 and 1 error!'; return; }
  255.    
  256.     document.getElementById("ErrorLabel").textContent = 'Calculating...';
  257.    
  258.     // Step 0 - set variables
  259.    
  260.     var MaxIterations = 500; // m = 500 points at least with results
  261.     var h = (b-a)/n; // step for points
  262.     var D = 0; // initial false distance (max dist of all points)
  263.     xl = new Array(n+1); // x*- exact
  264.     xu = new Array(n+1); // x*+ exact
  265.     // for trapezoid
  266.     t = new Array(n+1); // t(i)
  267.     xml = new Array(MaxIterations+1); // xml[0..m][0..n] - lower
  268.     for (var i = 0; i <= MaxIterations; i++) { xml[i] = new Array(n+1); }
  269.     xmu = new Array(MaxIterations+1); // xmu[0..m][0..n] - upper
  270.     for (var i = 0; i <= MaxIterations; i++) { xmu[i] = new Array(n+1); }
  271.     var el = new Array(n+1); // err-  approx - exact
  272.     var eu = new Array(n+1); // err+  approx - exact
  273.     // for optimal (middle rectangle)
  274.     to = new Array(n+1); // to(i)
  275.     xoml = new Array(MaxIterations+1); // xoml[0..m][0..n] - lower
  276.     for (var i = 0; i <= MaxIterations; i++) { xoml[i] = new Array(n+1); }
  277.     xomu = new Array(MaxIterations+1); // xomu[0..m][0..n] - upper
  278.     for (var i = 0; i <= MaxIterations; i++) { xomu[i] = new Array(n+1); }
  279.     var eol = new Array(n+1); // err-  approx - exact for opt
  280.     var eou = new Array(n+1); // err+  approx - exact for opt
  281.     var xtoml = new Array(MaxIterations+1); // xtoml[0..m][0..n] - lower
  282.     for (var i = 0; i <= MaxIterations; i++) { xtoml[i] = new Array(n+1); }
  283.     var xtomu = new Array(MaxIterations+1); // xtomu[0..m][0..n] - upper
  284.     for (var i = 0; i <= MaxIterations; i++) { xtomu[i] = new Array(n+1); }
  285.        
  286.     // initial values
  287.     for (var i = 0; i <= n; i++) { t[i] = a + i*h; }
  288.     for (var i = 1; i <= n; i++) { to[i] = a + (2*i-1)*(h/2); }
  289.     m = 0; // keep m < MaxIterations
  290.     mo = 0; // keep mo < MaxIterations
  291.     // parse functions once, outside of the loops
  292.     var Pglx = Parser.parse(glx);
  293.     var Pgux = Parser.parse(gux);
  294.     var Pkx = Parser.parse(kx);
  295.     var PHlx = Parser.parse(Hlx);
  296.     var PHux = Parser.parse(Hux);
  297.     var Pflx = Parser.parse(flx);
  298.     var Pfux = Parser.parse(fux);
  299.     var Pxlx = Parser.parse(xlx);
  300.     var Pxux = Parser.parse(xux);
  301.    
  302.     // Step 1 - x0(ti) m=0
  303.     for (var i = 0; i <= n; i++) {  // trapezoid
  304.         xml[0][i] = Pglx.evaluate({t: t[i], r: r});
  305.         xoml[0][i] = xml[0][i];
  306.         xmu[0][i] = Pgux.evaluate({t: t[i], r: r});
  307.         xomu[0][i] = xmu[0][i];
  308.     }
  309.     for (var i=1; i <= n; i++) { // optimal (middle finger)
  310.         xtoml[0][i] = Pglx.evaluate({t: to[i], r: r});
  311.         xtomu[0][i] = Pgux.evaluate({t: to[i], r: r});
  312.     }
  313.  
  314.     // Step 2 (the first iterative step)
  315.     // trapezoid
  316.     m = 1;
  317.     for (var i = 0; i <= n; i++) {
  318.         var sl = 0;  var su = 0;
  319.         for(var j = 1; j <= n; j++) {
  320.             sl = sl +
  321.                Pkx.evaluate({t: t[i], s: t[j-1]})
  322.                *
  323.                PHlx.evaluate({t: t[j-1], x: xml[m-1][j-1], r: r})
  324.             +
  325.                Pkx.evaluate({t: t[i], s: t[j]})
  326.                 *
  327.                PHlx.evaluate({t: t[j], x: xml[m-1][j], r: r});
  328.             su = su +
  329.                Pkx.evaluate({t: t[i], s: t[j-1]})
  330.                *
  331.                PHux.evaluate({t: t[j-1], x: xmu[m-1][j-1], r: r})
  332.             +
  333.                Pkx.evaluate({t: t[i], s: t[j]})
  334.                 *
  335.                PHux.evaluate({t: t[j], x: xmu[m-1][j], r: r});     
  336.         }
  337.         xml[m][i] = xml[0][i] + Pflx.evaluate({t: t[i], x: xml[m-1][i], r: r}) + (h/2)*sl;
  338.         xmu[m][i] = xmu[0][i] + Pfux.evaluate({t: t[i], x: xmu[m-1][i], r: r}) + (h/2)*su;
  339.     }
  340.     // optimal
  341.     mo = 1;
  342.     for (var i = 0; i <= n; i++) {
  343.         var sl = 0;  var su = 0;
  344.         var stl = 0; var stu = 0;
  345.         for(var j = 1; j <= n; j++) {
  346.             sl = sl +
  347.                Pkx.evaluate({t: t[i], s: to[j]})
  348.                *
  349.                PHlx.evaluate({t: to[j], x: xtoml[mo-1][j], r: r});
  350.             stl = stl +
  351.                Pkx.evaluate({t: to[i], s: to[j]})
  352.                *
  353.                PHlx.evaluate({t: to[j], x: xtoml[mo-1][j], r: r});
  354.             su = su +
  355.                Pkx.evaluate({t: t[i], s: to[j]})
  356.                *
  357.                PHux.evaluate({t: to[j], x: xtomu[mo-1][j], r: r});     
  358.             stu = stu +
  359.                Pkx.evaluate({t: to[i], s: to[j]})
  360.                *
  361.                PHux.evaluate({t: to[j], x: xtomu[mo-1][j], r: r});     
  362.         }
  363.         xoml[mo][i] = xoml[0][i] + Pflx.evaluate({t: t[i], x: xoml[mo-1][i], r: r}) + h*sl;
  364.         xomu[mo][i] = xomu[0][i] + Pfux.evaluate({t: t[i], x: xomu[mo-1][i], r: r}) + h*su;
  365.         if (i > 0) { xtoml[mo][i] = xtoml[0][i] + Pflx.evaluate({t: to[i], x: xtoml[mo-1][i], r: r}) + h*stl; }
  366.         if (i > 0) { xtomu[mo][i] = xtomu[0][i] + Pfux.evaluate({t: to[i], x: xtomu[mo-1][i], r: r}) + h*stu; }
  367.     }
  368.    
  369.     // Steps 3-4 (the generic iterative step)
  370.     // trapezoid
  371.     do {
  372.         m = m+1; // next iteration
  373.         if ( m > MaxIterations ) {
  374.             alert("Iterations exceeded "+MaxIterations+"! Stopped!"); return;
  375.         }
  376.         for (var i = 0; i <= n; i++) {
  377.             var sl = 0;  var su = 0;
  378.             for(var j = 1; j <= n; j++) {
  379.                 sl = sl +
  380.                    Pkx.evaluate({t: t[i], s: t[j-1]})
  381.                     *
  382.                    PHlx.evaluate({t: t[j-1], x: xml[m-1][j-1], r: r})
  383.                 +
  384.                    Pkx.evaluate({t: t[i], s: t[j]})
  385.                     *
  386.                    PHlx.evaluate({t: t[j], x: xml[m-1][j], r: r});
  387.                 su = su +
  388.                    Pkx.evaluate({t: t[i], s: t[j-1]})
  389.                     *
  390.                    PHux.evaluate({t: t[j-1], x: xmu[m-1][j-1], r: r})
  391.                 +
  392.                    Pkx.evaluate({t: t[i], s: t[j]})
  393.                     *
  394.                    PHux.evaluate({t: t[j], x: xmu[m-1][j], r: r});     
  395.             }
  396.             xml[m][i] = xml[0][i] + Pflx.evaluate({t: t[i], x: xml[m-1][i], r: r}) + (h/2)*sl;
  397.             xmu[m][i] = xmu[0][i] + Pfux.evaluate({t: t[i], x: xmu[m-1][i], r: r}) + (h/2)*su;
  398.         }
  399.         // calculate D as max(D(x(m,t(i)), x(m-1,t(i))) for i = 0..n
  400.         D = 0;
  401.         for (var i = 0; i <= n; i++) {
  402.             var Di = Math.max(Math.abs(xml[m][i] - xml[m-1][i]), Math.abs(xmu[m][i] - xmu[m-1][i]));
  403.             if ( Di > D ) { D = Di };
  404.         }
  405.     } while ( (D >= eps) && (m < MaxIterations) );
  406.     // possible also check m is reasonable to avoid endless looping if no convergence
  407.     if ( m >= MaxIterations)
  408.     {
  409.         alert("Endless loop detected (>"+MaxIterations+" iterations) in trapezoid!");
  410.         return;
  411.     }
  412.     // optimal (middle rectangle)
  413.     do {
  414.         mo = mo+1; // next iteration
  415.         if ( mo >= MaxIterations ) {
  416.             alert("Iterations exceeded "+MaxIterations+"! Stopped!"); return;
  417.         }
  418.         for (var i = 0; i <= n; i++) {
  419.             var sl = 0;  var su = 0;
  420.             var stl = 0; var stu = 0;
  421.             for(var j = 1; j <= n; j++) {
  422.                 sl = sl +
  423.                    Pkx.evaluate({t: t[i], s: to[j]})
  424.                    *
  425.                    PHlx.evaluate({t: to[j], x: xtoml[mo-1][j], r: r});
  426.                 stl = stl +
  427.                    Pkx.evaluate({t: to[i], s: to[j]})
  428.                    *
  429.                    PHlx.evaluate({t: to[j], x: xtoml[mo-1][j], r: r});
  430.                 su = su +
  431.                    Pkx.evaluate({t: t[i], s: to[j]})
  432.                    *
  433.                    PHux.evaluate({t: to[j], x: xtomu[mo-1][j], r: r});     
  434.                 stu = stu +
  435.                    Pkx.evaluate({t: to[i], s: to[j]})
  436.                    *
  437.                    PHux.evaluate({t: to[j], x: xtomu[mo-1][j], r: r});     
  438.             }
  439.             xoml[mo][i] = xoml[0][i] + Pflx.evaluate({t: t[i], x: xoml[mo-1][i], r: r}) + h*sl;
  440.             xomu[mo][i] = xomu[0][i] + Pfux.evaluate({t: t[i], x: xomu[mo-1][i], r: r}) + h*su;
  441.             if (i > 0) xtoml[mo][i] = xtoml[0][i] + Pflx.evaluate({t: to[i], x: xtoml[mo-1][i], r: r}) +  h*stl;
  442.             if (i > 0) xtomu[mo][i] = xtomu[0][i] + Pfux.evaluate({t: to[i], x: xtomu[mo-1][i], r: r}) +  h*stu;
  443.         }
  444.         // calculate D
  445.         D = 0;
  446.         for (var i = 0; i <= n; i++) {
  447.             var Di = Math.max(Math.abs(xoml[mo][i] - xoml[mo-1][i]), Math.abs(xomu[mo][i] - xomu[mo-1][i]));
  448.             if ( Di > D ) { D = Di };
  449.         }
  450.     } while ( (D >= eps) && (mo < MaxIterations) );
  451.     // possible also check m is reasonable to avoid endless looping if no convergence
  452.     if ( mo >= MaxIterations)
  453.     {
  454.         alert("Endless loop detected (>"+MaxIterations+" iterations) in optimal formula!");
  455.         return;
  456.     }
  457.    
  458.     Calculated = m > 0; // flag for the graphics plot
  459.    
  460.     // calculate the exact solution
  461.     for (var i = 0; i <= n; i++) {
  462.         xl[i] = Pxlx.evaluate({t: t[i], r: r});
  463.         el[i] = Math.abs(xl[i] - xml[m][i]);
  464.         eol[i] = Math.abs(xl[i] - xoml[mo][i]);
  465.         xu[i] = Pxux.evaluate({t: t[i], r: r});
  466.         eu[i] = Math.abs(xu[i] - xmu[m][i]);
  467.         eou[i] = Math.abs(xu[i] - xomu[mo][i]);
  468.     }
  469.  
  470.     // draw a table and plot a graphics
  471.     document.getElementById("ErrorLabel").textContent = 'Done calculation...';
  472.  
  473.     var errors ='<caption>Errors</caption><tr><th>t<sub>i</sub></th><th>e<sub>i-</sub></th><th>eo<sub>i-</sub></th><th>e<sub>i+</sub></th><th>eo<sub>i+</sub></th></tr>';
  474.     for (var i = 0; i <= n; i++) {
  475.         errors+='<tr><td>'+myFixed(t[i],2)+'</td><td>'+el[i].toFixed(6)+'</td><td>'+eol[i].toFixed(6)+'</td><td>'+eu[i].toFixed(6)+'</td><td>'+eou[i].toFixed(6)+'</td></tr>';
  476.     }
  477.  
  478.     var values ='<caption>Values</caption><tr><th>t<sub>i</sub></th><th>x<sub>i-</sub></th><th>xc<sub>i-</sub></th><th>xo<sub>i-</sub></th><th>x<sub>i+</sub></th><th>xc<sub>i+</sub></th><th>xo<sub>i+</sub></th></tr>';
  479.     for (var i = 0; i <= n; i++) {
  480.         values+='<tr><td>'+myFixed(t[i],2)+'</td><td>'+xl[i].toFixed(6)+'</td><td>'+xml[m][i].toFixed(6)+'</td><td>'+xoml[mo][i].toFixed(6)+'</td><td>'+xu[i].toFixed(6)+'</td><td>'+xmu[m][i].toFixed(6)+'</td><td>'+xomu[mo][i].toFixed(6)+'</td></tr>';
  481.     }
  482.  
  483.     document.getElementById("ResultLabel1").innerHTML = '<center>Numerical results for n='+n+', r='+r.toFixed(2)+' (iterations: '+m+' classical, '+mo+' optimal)</center>';
  484.     document.getElementById("ResultsErrors").innerHTML = errors;
  485.     document.getElementById("ResultsValues").innerHTML = values;
  486.    
  487.     document.getElementById("ResultLabel2").innerHTML = '';
  488.     document.getElementById('animated-result').style.display = ''; // show the result
  489.    
  490. } // catch the error and show the eror message
  491. catch(err) {
  492.     var vDebug = "";
  493.     for (var prop in err)
  494.     {  
  495.        vDebug += "property: "+ prop+ " ["+ err[prop]+ "], ";
  496.     }
  497.     vDebug += "[" + err.toString() + "]";
  498.     document.getElementById('animated-result').style.display = 'none'; // hide result
  499.     document.getElementById("ErrorLabel").textContent = 'Error: ' + err.message +
  500.       ' ' + vDebug;}   
  501. }
  502.  
  503. </script>
  504.  
  505. </p>
  506.  
  507. </body>
  508. </html>
Advertisement
Add Comment
Please, Sign In to add comment
Advertisement
Public Pastes
Advertisement
We use cookies for various purposes including analytics. By continuing to use Pastebin, you agree to our use of cookies as described in the Cookies Policy.  OK, I Understand
Not a member of Pastebin yet?
Sign Up, it unlocks many cool features!