Difference between revisions of "Differential equations"
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Display solutions of the ordinary differential equation | Display solutions of the ordinary differential equation | ||
− | :<math> | + | :<math> y'= f(x,y)</math> |
with initial value <math>(x_0,y_0)</math>. | with initial value <math>(x_0,y_0)</math>. | ||
<html> | <html> | ||
<form> | <form> | ||
− | f( | + | f(x,y)=<input type="text" id="odeinput" value="(2-x)*y"><input type=button value="ok" onclick="doIt()"> |
</form> | </form> | ||
</html> | </html> | ||
Line 46: | Line 46: | ||
<source lang="xml"> | <source lang="xml"> | ||
<form> | <form> | ||
− | f( | + | f(x,y)=<input type="text" id="odeinput" value="(2-x)*y"><input type=button value="ok" onclick="doIt()"> |
</form> | </form> | ||
</source> | </source> |
Revision as of 12:28, 15 July 2010
Display solutions of the ordinary differential equation
- [math] y'= f(x,y)[/math]
with initial value [math](x_0,y_0)[/math].
See also
- Lotka-Volterra equations
- Epidemiology: The SIR model
- Population growth models
- Autocatalytic process
- Logistic process
The underlying JavaScript code
<form>
f(x,y)=<input type="text" id="odeinput" value="(2-x)*y"><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 txt = JXG.GeonextParser.geonext2JS(document.getElementById("odeinput").value);
f = new Function("t", "xx", "var x = xx[0]; var y = " + txt + "; 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();