Systems of differential equations: Difference between revisions
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function doIt() { | function doIt() { | ||
var | var txt1 = JXG.GeonextParser.geonext2JS(document.getElementById("odeinput1").value); | ||
f = new Function("x", "yy", "var | var txt2 = JXG.GeonextParser.geonext2JS(document.getElementById("odeinput2").value); | ||
f = new Function("x", "yy", "var y1 = yy[0], y1 = yy[1]; var z1 = " + txt1 + "; var z2 = " + txt2 + "; return [z1,z2];"); | |||
brd.update(); | brd.update(); | ||
} | } | ||
function ode() { | function ode() { | ||
return JXG.Math.Numerics.rungeKutta(JXG.Math.Numerics.predefinedButcher.Heun, [P1.Y()], [P1.X(), P1.X()+N.Value()], 200, f); | return JXG.Math.Numerics.rungeKutta(JXG.Math.Numerics.predefinedButcher.Heun, [P1.Y(),P2.Y()], [P1.X(), P1.X()+N.Value()], 200, f); | ||
} | } | ||
var | var g1 = brd.createElement('curve', [[0],[0]], {strokeColor:'red', strokeWidth:'2px'}); | ||
var g2 = brd.createElement('curve', [[0],[0]], {strokeColor:'black', strokeWidth:'2px'}); | |||
g1.updateDataArray = function() { | |||
var data = ode(); | var data = ode(); | ||
var h = N.Value()/200; | var h = N.Value()/200; | ||
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this.dataX[i] = P1.X()+i*h; | this.dataX[i] = P1.X()+i*h; | ||
this.dataY[i] = data[i][0]; | this.dataY[i] = data[i][0]; | ||
} | |||
}; | |||
g2.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] = P2.X()+i*h; | |||
this.dataY[i] = data[i][1]; | |||
} | } | ||
}; | }; | ||
doIt(); | doIt(); | ||
</jsxgraph> | </jsxgraph> | ||
Revision as of 08:50, 21 July 2010
Display solutions of the ordinary differential equation
- [math]\displaystyle{ y_1'= f_1(x,y_1,y_2) }[/math]
- [math]\displaystyle{ y_2'= f_2(x,y_1,y_2) }[/math]
with initial values [math]\displaystyle{ (x_0,y_1) }[/math], [math]\displaystyle{ (x_0,y_2) }[/math].
