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


Sean,

Plot[Evaluate[x[t] + y[t] /. solution], {t, 0, 25},
    PlotPoints -> 1000, PlotRange -> All,
    Frame -> True,
    FrameLabel -> {t, x + y}];

ParametricPlot[Evaluate[{y[t], x[t] + z[t]} /. solution], {t, 0, 25},
    PlotPoints -> 1000, PlotRange -> All,
    Frame -> True,
    FrameLabel -> {y, x + z}];

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/ 

From: sean kim [mailto:sean_incali at yahoo.com]
To: mathgroup at smc.vnet.net

hello group. 

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? 

as always any and all thoughts are appreciated. 

thank you all in advance

sean



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