Re: animation of the PDE
- To: mathgroup at smc.vnet.net
- Subject: [mg132331] Re: animation of the PDE
- From: Любовь Тупикина <lyubov78 at gmail.com>
- Date: Tue, 11 Feb 2014 02:57:22 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- Delivered-to: l-mathgroup@wolfram.com
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- References: <b2fc44751be24af4850802802e9aa585@DB3PR07MB089.eurprd07.prod.outlook.com>
Dear Alexei! Thank you so much! Yes, with this equation it works. I did not put the equations because they are long. Maybe I needed to include them into the module or something... Here is my system: eps := 1; B0 := 1.2; om := 0.4; tet := 1.5; k := 0.5; c := 0.12; psi[x[p], y[p], p] = 1 - Tanh[y/(Sqrt[ 1 + k^2 (B0 + eps Cos[om p + tet])^2 (Sin[ k (x - c p)])^2]) - ((B0 + eps Cos[om p + tet]) Cos[ k (x - c p)]/ Sqrt[1 + k^2 (B0 + eps Cos[om p + tet])^2 (Sin[k (x - c p)])^2])] %PDE, which I am solving and animating(*) Animate[ParametricPlot[ Evaluate[{y[p], x[p]} /. NDSolve[{D[psi[x[p], y[p], p], y[p]] = x'[p], D[psi[x[p], y[p], p], x[p]] = y'[p], 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}] But it doesn't make the animation of the trajectory x[p], y[p]. "Equation or list of equations expected instead of \ \!\(\*SuperscriptBox[\"x\", \"\[Prime]\", MultilineFunction->None][p]\) in the first argument \ {\!\(\*SuperscriptBox[\"x\", \"\[Prime]\", MultilineFunction->None][p]\),\!\(\*SuperscriptBox[\"y\", \"\[Prime]\", MultilineFunction->None][p]\),x[1]==-1,y[1]==-1}" %------------------------------------------------------------------------------------------------------ p.s. Actually, I was focusing on trying to show several solutions (without any animation) of this PDE (*) depending on the initial conditions {x[1] == i, y[1] == j}, like in cycle: For[i = 1, i < 10, i++, {ParametricPlot[ Evaluate[{y[p], x[p]} /. NDSolve[{D[psi[x[p], y[p], p], y[p]] = x'[p], D[psi[x[p], y[p], p], x[p]] = y'[p], x[1] == i, y[1] == i}, {y[p], x[p]}, {p, 1, Tp}]], {p, 1, Tp}, PlotRange -> {{-2, 2}, {-2, 2}}]}] But it also gave me mistakes, some are like in first case: NDSolve::deqn: "Equation or list of equations expected instead of \!\(\*SuperscriptBox[\"x\", \"\[Prime]\", MultilineFunction->None][p]\) in the first argument {\!\(\*SuperscriptBox[\"x\", \"\[Prime]\", MultilineFunction->None][p], \*SuperscriptBox[\"y\", \"\[Prime]\", MultilineFunction->None][p], x[1] == 1, y[1] == 1\)}." Can you please tell, if the second case is possible to visualise (I mean, to make a loop through initial conditions). Thank you very much! 2014-02-10 9:20 GMT+01:00 Alexei Boulbitch <Alexei.Boulbitch at iee.lu>: > Hola! > > I was using Mathematica to visualise trajectories of x[p],y[p] depending > on p. > Is it possible? > > Talking about "it's simple > 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 > > >