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MathGroup Archive 2004

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Animating Solutions of NDSolve with respect to Initial Conditions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg52520] Animating Solutions of NDSolve with respect to Initial Conditions
  • From: mathma18 at hotmail.com (Narasimham G.L.)
  • Date: Tue, 30 Nov 2004 05:24:48 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

To see all circularly bent shapes of a strip fixed at one end it is
animated as follows:

<< Graphics`Animation`
MovieParametricPlot[{Sin[t*s]/t , (1 - Cos[t*s])/t}, {s, 0, 2 Pi},
{t, -1,1}, Frames -> 20, Axes -> False, AspectRatio -> Automatic, 
PlotRange -> {{-3, 7}, {-3, 7}}];

Like the above and unlike the example below where solutions are
superimposed in Show mode in a single frame, I like to animate an
NDSolve output to varoious Boundary Conditions to see their effect
dynamically in separate frames. How can this be done?

yvar = y /. 
First /@ (NDSolve[{y'''[t] + y[t] == 0, y[0] == #1, y'[0] == #2, 
y''[0] == #3}, y, {t, 0, 2 Pi}] & @@@ {{5, 1, -2}, {5, 
1, -1}, {5, 1, 0}, {5, 1, 1}, {5, 1, 2}});
Plot[Evaluate[#[t] & /@ yvar], {t, 0, 5}];


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