Difference between revisions of "Differential equations"
From JSXGraph Wiki
Jump to navigationJump to searchA WASSERMANN (talk | contribs) |
A WASSERMANN (talk | contribs) |
||
Line 1: | Line 1: | ||
Display solutions of the ordinary differential equation | Display solutions of the ordinary differential equation | ||
− | <math> | + | :<math> x'= f(t,x)</math> |
with initial value <math>(x_0,y_0)</math>. | with initial value <math>(x_0,y_0)</math>. | ||
<html> | <html> | ||
Line 37: | Line 37: | ||
===The underlying JavaScript code=== | ===The underlying JavaScript code=== | ||
+ | <source lang="xml"> | ||
+ | <form> | ||
+ | f(t,x)=<input type="text" id="odeinput" value="(2-t)*x"><input type=button value="ok" onclick="doIt()"> | ||
+ | </form> | ||
+ | </source> | ||
<source lang="javascript"> | <source lang="javascript"> | ||
+ | var brd = JXG.JSXGraph.initBoard('jxgbox', {axis:true, boundingbox:[-11,11,11,-11]}); | ||
+ | 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)'}); | ||
+ | |||
+ | function doIt() { | ||
+ | var t = JXG.GeonextParser.geonext2JS(document.getElementById("odeinput").value); | ||
+ | f = new Function("t", "xx", "var x = xx[0]; var y = " + t + "; return [y]"); | ||
+ | brd.update(); | ||
+ | } | ||
+ | |||
+ | function ode() { | ||
+ | return JXG.Math.Numerics.rungeKutta(JXG.Math.Numerics.predefinedButcher.Heun, [P.Y()], [P.X(), P.X()+N.Value()], 200, f); | ||
+ | } | ||
+ | |||
+ | var g = brd.createElement('curve', [[0],[0]], {strokeColor:'red', strokeWidth:'2px'}); | ||
+ | g.updateDataArray = function() { | ||
+ | var data = ode(); | ||
+ | var h = N.Value()/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(); | ||
</source> | </source> | ||
[[Category:Examples]] | [[Category:Examples]] | ||
[[Category:Calculus]] | [[Category:Calculus]] |
Revision as of 16:21, 14 July 2010
Display solutions of the ordinary differential equation
- [math] x'= f(t,x)[/math]
with initial value [math](x_0,y_0)[/math].
The underlying JavaScript code
<form>
f(t,x)=<input type="text" id="odeinput" value="(2-t)*x"><input type=button value="ok" onclick="doIt()">
</form>
var brd = JXG.JSXGraph.initBoard('jxgbox', {axis:true, boundingbox:[-11,11,11,-11]});
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)'});
function doIt() {
var t = JXG.GeonextParser.geonext2JS(document.getElementById("odeinput").value);
f = new Function("t", "xx", "var x = xx[0]; var y = " + t + "; return [y]");
brd.update();
}
function ode() {
return JXG.Math.Numerics.rungeKutta(JXG.Math.Numerics.predefinedButcher.Heun, [P.Y()], [P.X(), P.X()+N.Value()], 200, f);
}
var g = brd.createElement('curve', [[0],[0]], {strokeColor:'red', strokeWidth:'2px'});
g.updateDataArray = function() {
var data = ode();
var h = N.Value()/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();