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MathGroup Archive 2004

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Re: adding subset of interpolating function from a system of ODE

  • To: mathgroup at smc.vnet.net
  • Subject: [mg45864] Re: adding subset of interpolating function from a system of ODE
  • From: bobhanlon at aol.com (Bob Hanlon)
  • Date: Wed, 28 Jan 2004 05:19:02 -0500 (EST)
  • References: <bv5e79$t28$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

solution=NDSolve[{
        Derivative[1][x][t]==-y[t]-z[t],
        x[0]==-0.04,
        Derivative[1][y][t]==x[t]+0.425*y[t],
        y[0]==-0.3,
        Derivative[1][z][t]==2-(4-x[t])*z[t],
        z[0]==0.52},
      {x[t],y[t],z[t]},{t,0,25}];

ParametricPlot3D[
    Evaluate[{x[t],y[t],z[t]}/.solution],
    {t,0,25},PlotPoints->1000,PlotRange->All];

Plot[x[t]+y[t] /. solution, {t,0,25}];

ParametricPlot[{y[t], x[t]+z[t]} /. solution, 
    {t, 0, 25}, PlotRange->All];


Bob Hanlon

In article <bv5e79$t28$1 at smc.vnet.net>, sean_incali at yahoo.com (sean kim) wrote:

<< Please consider the lorenz system for example. 

In[2]:=
solution=NDSolve[{Derivative[1][x][t]\[Equal]-y[t]-z[t],x[0]\[Equal]-0.04,
        Derivative[1][y][t]\[Equal]x[t]+0.425*y[t],y[0]\[Equal]-0.3,
        Derivative[1][z][t]\[Equal]2-(4-x[t])*z[t],z[0]\[Equal]0.52},{x[t],
        y[t],z[t]},{t,0,25}];

ParametricPlot3D[Evaluate[{x[t],y[t],z[t]}/.solution],{t,0,25},
    PlotPoints -> 1000,PlotRange ->All];

above shows a parametric plot of x, y and z. 

but let's say for some reason I want to plot the following..

x+y vs time
x+z vs  y

how do I achieve this?  is this possible in mathematica? 



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