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Re: Terminate NDSolve by a condition

  • To: mathgroup at smc.vnet.net
  • Subject: [mg123622] Re: Terminate NDSolve by a condition
  • From: Bob Hanlon <hanlonr357 at gmail.com>
  • Date: Tue, 13 Dec 2011 05:42:48 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <201112121142.GAA12764@smc.vnet.net>

eqns = {x'[t] == -Sin[t], y'[t] == Cos[t], x[0] == 1, y[0] == 0};

sol2[tf_?NumericQ] :=
 NDSolve[eqns, {x, y}, {t, 0, tf}][[1]]

p = tf /. FindRoot[(x[tf] /. sol2[tf]) == 1, {tf, 5}] // Quiet

6.28319

p = RootApproximant[p/Pi] Pi

2*Pi

sol = NDSolve[eqns, {x, y}, {t, 0, p}];

Plot[Evaluate[x[t] /. sol], {t, 0, p}]

ParametricPlot[Evaluate[{x[t], y[t]} /. sol], {t, 0, p}]


Bob Hanlon


On Mon, Dec 12, 2011 at 6:42 AM, Sam Takoy <sam.takoy at yahoo.com> wrote:
> Hi,
>
> Suppose I'm solving a system of ODE's for x[t] and y[t] and I know
> that there is a periodic solution, but beyond that I know nothing, not
> even how long the period is. So I want to stop NDSolve when x repeats
> a certain value. Here's an example:
>
> sol = NDSolve[{x'[t] == -Sin[t], y'[t] == Cos[t], x[0] == 1, y[0] ==
> 0}, {x, y}, {t, 0, 6}];
> ParametricPlot[Evaluate[{x[t], y[t]} /. sol], {t, 0, 6}]
>
> This solution goes from 0 to 6, but I want it to go from 0 until x(t)
> = 1 again.
>
> What's the best way to accomplish this?
>
> Many thanks in advance,
>
> Sam



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