Re: animation of the PDE

• To: mathgroup at smc.vnet.net
• Subject: [mg132330] Re: animation of the PDE
• From: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>
• Date: Tue, 11 Feb 2014 02:57:02 -0500 (EST)
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• Delivered-to: l-mathgroup@wolfram.com
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```Hola!

I was using Mathematica to visualise trajectories of x[p],y[p] depending on p.
Is it possible?

to animate the parametric plot of them by using ParametricPlot inside
Animate."

But I cannot animate the NDSolve using ParametricPlot.
Can you please tell me why I get errors like "NDSolve::dsvar: 1.0011952113073699` cannot be used as a variable. ":

Animate[
ParametricPlot[
{Evaluate[{y[p], x[p]} /. sol =
NDSolve[...some equation type D[f1[x[p],y[p],p] = -D[x[p], p],
f2[x[p],y[p],p] = -D[y[p], p]
x[1] == -1, y[1] == -1}, {y[p], x[p]}, {p, 1, Tp}]]},
{p, 1, Tp}], {Tp, 1, 100}]

Thank you!

Hi, Ljuba,

Your code has nothing wrong in it except that you kept it without a precise equation. Have a look at the code below.
I have only written down a simple equation containing a focus into your code:
x'[p] == -y[p] - x[p]^3,
y'[p] == x[p] - y[p]^3

The animation appears to be rather spectacular:

Animate[
ParametricPlot[
Evaluate[{y[p], x[p]} /.
NDSolve[{x'[p] == -y[p] - x[p]^3, y'[p] == x[p] - y[p]^3,
x[1] == -1, y[1] == -1}, {y[p], x[p]}, {p, 1, Tp}]], {p, 1,
Tp}, PlotRange -> {{-2, 2}, {-2, 2}}] /. Line -> Arrow, {Tp, 1,
30}]

Try it. Have fun.

Alexei

Alexei BOULBITCH, Dr., habil.
IEE S.A.
ZAE Weiergewan,
11, rue Edmond Reuter,
L-5326 Contern, LUXEMBOURG

Office phone :  +352-2454-2566
Office fax:       +352-2454-3566
mobile phone:  +49 151 52 40 66 44

e-mail: alexei.boulbitch at iee.lu

```

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