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<html>
<head>
<title>Slope fields and the Runge-Kutta method</title>
<link rel="stylesheet" type="text/css" href="/jsxgraph/distrib/jsxgraph.css" />
<script type="text/javascript" src="../distrib/jsxgraphcore.js"></script>
</head>
<body>
<form>
dy / dx = f(x,y) = <input type="text" id="odeinput" value="(2-x)*y""><input type=button value="ok" onclick="doIt()"> <br />
Segment length = <input name="SegmentLength" id="SegmentLength" size="20" value="0.4" type="text"><input type=button value="ok" onclick="doIt()"> <br />
x min = <input id="Xmin" size="10" value="-4" type="text"><input type=button value="ok" onclick="doIt()">
x max = <input id="Xmax" size="10" value="4" type="text"><input type=button value="ok" onclick="doIt()"> <br />
</form>
<div id='jxgbox' class='jxgbox' style='width:500px; height:500px;'></div>
<script type='text/javascript'>
var length = 0.4;
var xmin = -4;
var xmax = 4;
var xsep = 0.5;
var xnum = Math.ceil((xmax-xmin)/xsep);
var ymin = -4;
var ymax = 4;
var ysep = 0.5;
var ynum = Math.ceil((ymax-ymin)/ysep);
var brd = JXG.JSXGraph.initBoard('jxgbox', {axis:true, boundingbox:[xmin,ymax,xmax,ymin]});
//var N = brd.create('slider',[[-7,9.5],[7,9.5],[-15,10,15]], {name:'N'});
//var P = brd.create('point',[0,1], {name:'(x_0,y_0)'});
var N = 10;
var P;
function doIt() {
JXG.JSXGraph.freeBoard(brd);
length = parseFloat(document.getElementById('SegmentLength').value);
xmin = parseFloat(document.getElementById('Xmin').value);
xmax = parseFloat(document.getElementById('Xmax').value);
brd = JXG.JSXGraph.initBoard('jxgbox', {axis:true, boundingbox:[xmin,ymax,xmax,ymin]});
var txt = JXG.GeonextParser.geonext2JS(document.getElementById("odeinput").value);
f = new Function("x", "yy", "var y = yy[0]; var z = " + txt + "; return [z];"); // f is a global variable
brd.suspendUpdate();
P = brd.create('point',[0,1], {name:'P'});
plotFunction();
slopefield(f);
brd.unsuspendUpdate();
}
function ode() {
return JXG.Math.Numerics.rungeKutta('heun', [P.Y()], [P.X(), P.X()+N], 200, f);
}
function slope(x,y,f) {
return f(x,[y])[0];
}
function slopefield(f) {
var xval, yval;
for (var i=0;i<=xnum;i++) {
xval = xmin + i*xsep;
for (var j=0;j<=ynum;j++) {
yval = ymin + j*ysep;
brd.create('segment',[
[xval-0.5*length*Math.cos(Math.atan( slope(xval,yval,f) )), yval-0.5*length*Math.sin(Math.atan( slope(xval,yval,f) ))],
[xval+0.5*length*Math.cos(Math.atan( slope(xval,yval,f) )), yval+0.5*length*Math.sin(Math.atan( slope(xval,yval,f) ))]
],
{strokeWidth:1, dash:0});
}
}
}
function plotFunction() {
var g = brd.create('curve', [[0],[0]], {strokeColor:'red', strokeWidth:'2'});
g.updateDataArray = function() {
var data = ode();
var h = N/200;
this.dataX = [];
this.dataY = [];
for(var i=0; i<data.length; i++) {
this.dataX[i] = P.X()+i*h;
this.dataY[i] = data[i][0];
}
};
};
doIt();
</script>
<script type="text/javascript">
// var slope = "";
// var dydx = JXG.GeonextParser.geonext2JS(document.getElementById("odeinpt").value);
// var txt = JXG.GeonextParser.geonext2JS(document.getElementById("odeinput").value);
// document.write(eval(txt.replace(/x/g,5).replace(/y/g,3)));
// slope = eval(dydx.replace(/x/g,xval).replace(/y/g,yval));
//var dydx = "y*(2-y)";
//var yvalue = 3;
//dydx = dydx.replace(/y/g,yvalue);
//document.write(dydx);
//document.write(parseFloat(dydx));
//document.write(eval(dydx));
// var txt = JXG.GeonextParser.geonext2JS(document.getElementById("odeinput").value);
//document.write(eval(txt.replace(/x/g,5).replace(/y/g,3)));
/*
function parser(dydx) {
dydx = dydx.replace(/cos/g,"Math.cos");
dydx = dydx.replace(/sin/g,"Math.sin");
dydx = dydx.replace(/tan/g,"Math.tan");
dydx = dydx.replace(/sec/g,"1/Math.cos");
dydx = dydx.replace(/csc/g,"1/Math.sin");
dydx = dydx.replace(/cot/g,"1/Math.tan");
dydx = dydx.replace(/acos/g,"Math.acos");
dydx = dydx.replace(/asin/g,"Math.asin");
dydx = dydx.replace(/atan/g,"Math.atan");
dydx = dydx.replace(/log/g,"Math.LOG10E*Math.log"); // base 10
dydx = dydx.replace(/ln/g,"Math.log"); // base e
dydx = dydx.replace(/sqrt/g,"Math.sqrt"); // base e
dydx = dydx.replace(/abs/g,"Math.abs"); // base e
dydx = dydx.replace(/pi/g,"Math.PI"); // base e
dydx = dydx.replace(/PI/g,"Math.PI"); // base e
dydx = dydx.replace(/Pi/g,"Math.PI"); // base e
dydx = dydx.replace(/\[/g,"("); // replace [ by ( etc.
dydx = dydx.replace(/\]/g,")");
dydx = dydx.replace(/\{/g,"(");
dydx = dydx.replace(/\}/g,")");
return dydx;
}
*/
//Sequence[Sequence[Segment[(X - 0.5 length cos(atan(Y (2 - Y))), Y - 0.5 length sin(atan(Y (2 - Y)))), (X + 0.5 length cos(atan(Y (2 - Y))), Y + 0.5 length sin(atan(Y (2 - Y))))], X, xmin, xmax, xsep], Y, ymin, ymax, ysep]
</script>
</body>
</html>
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