       Re: Animating Solutions of NDSolve with respect to Initial Conditions

• To: mathgroup at smc.vnet.net
• Subject: [mg52543] Re: Animating Solutions of NDSolve with respect to Initial Conditions
• From: Peter Pein <petsie at arcor.de>
• Date: Wed, 1 Dec 2004 05:58:20 -0500 (EST)
• References: <cohjd6\$1of\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Narasimham G.L. wrote:

> 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 == #1, y' == #2,
> y'' == #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}];
>
You nearly got it:

yvar = y /.
First /@ (NDSolve[{y'''[t] + y[t] == 0, y == #1, y' == #2,
y'' == #3}, y, {t, 0, 2 Pi}] & @@@
Table[{5, 1, p}, {p, -2, 2, .1}]);
Plot[#, {t, 0, 5}, PlotRange -> {-40, 10}] & /@
Evaluate[#[t] & /@ yvar];

--
Peter Pein
10245 Berlin

```

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