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}];