Difference between revisions of "Systems of differential equations"

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Line 17: Line 17:
  
 
function doIt() {
 
function doIt() {
   var txt = JXG.GeonextParser.geonext2JS(document.getElementById("odeinput1").value);
+
   var txt1 = JXG.GeonextParser.geonext2JS(document.getElementById("odeinput1").value);
   f = new Function("x", "yy", "var y = yy[0]; var z = " + txt + "; return [z]");
+
  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 g = brd.createElement('curve', [[0],[0]], {strokeColor:'red', strokeWidth:'2px'});
+
var g1 = brd.createElement('curve', [[0],[0]], {strokeColor:'red', strokeWidth:'2px'});
g.updateDataArray = function() {
+
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;
Line 35: Line 37:
 
         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 09:50, 21 July 2010

Display solutions of the ordinary differential equation

[math] y_1'= f_1(x,y_1,y_2)[/math]
[math] y_2'= f_2(x,y_1,y_2)[/math]

with initial values [math](x_0,y_1)[/math], [math](x_0,y_2)[/math].

f1(x,y1,y2)=
f2(x,y1,y2)=