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> y'= f( | + | :<math> y'= f(t,y)</math> |
with initial value <math>(x_0,y_0)</math>. | with initial value <math>(x_0,y_0)</math>. | ||
<html> | <html> | ||
Line 58: | Line 58: | ||
var brd = JXG.JSXGraph.initBoard('jxgbox', {axis:true, boundingbox:[-11,11,11,-11]}); | 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 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 P = brd.create('point',[0,1], {name:'(x_0, y_0)'}); |
+ | var f; | ||
function doIt() { | function doIt() { | ||
− | var | + | var snip = brd.jc.snippet(document.getElementById("odeinput").value, true, 'x, y'); |
− | f = | + | f = function (x, yy) { |
+ | return [snip(x, yy[0])]; | ||
+ | } | ||
brd.update(); | brd.update(); | ||
} | } | ||
Line 74: | Line 77: | ||
var data = ode(); | var data = ode(); | ||
var h = N.Value()/200; | var h = N.Value()/200; | ||
+ | var i; | ||
this.dataX = []; | this.dataX = []; | ||
this.dataY = []; | this.dataY = []; | ||
− | for( | + | for(i=0; i<data.length; i++) { |
this.dataX[i] = P.X()+i*h; | this.dataX[i] = P.X()+i*h; | ||
this.dataY[i] = data[i][0]; | this.dataY[i] = data[i][0]; | ||
} | } | ||
}; | }; | ||
− | doIt(); | + | doIt();</source> |
− | </source> | ||
[[Category:Examples]] | [[Category:Examples]] | ||
[[Category:Calculus]] | [[Category:Calculus]] |
Revision as of 12:27, 19 January 2017
Display solutions of the ordinary differential equation
- [math] y'= f(t,y)[/math]
with initial value [math](x_0,y_0)[/math].
See also
- Systems of differential equations
- Lotka-Volterra equations
- Epidemiology: The SIR model
- Population growth models
- Autocatalytic process
- Logistic process
- Paul Pearson has written a very nice variation: Slope fields and solution curves (using the Runge-Kutta)
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)'});
var f;
function doIt() {
var snip = brd.jc.snippet(document.getElementById("odeinput").value, true, 'x, y');
f = function (x, yy) {
return [snip(x, yy[0])];
}
brd.update();
}
function ode() {
return JXG.Math.Numerics.rungeKutta('heun', [P.Y()], [P.X(), P.X()+N.Value()], 200, f);
}
var g = brd.create('curve', [[0],[0]], {strokeColor:'red', strokeWidth:2});
g.updateDataArray = function() {
var data = ode();
var h = N.Value()/200;
var i;
this.dataX = [];
this.dataY = [];
for(i=0; i<data.length; i++) {
this.dataX[i] = P.X()+i*h;
this.dataY[i] = data[i][0];
}
};
doIt();