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Re: Problem involving NDSolve
*To*: mathgroup at smc.vnet.net
*Subject*: [mg86851] Re: Problem involving NDSolve
*From*: "David Park" <djmpark at comcast.net>
*Date*: Sun, 23 Mar 2008 01:03:28 -0500 (EST)
*References*: <fs26qf$9l$1@smc.vnet.net>
I posted a solution to this problem on 12 March 08.
--
David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/
"Grandpa" <acloninger at wustl.edu> wrote in message
news:fs26qf$9l$1 at smc.vnet.net...
> So here's my dilemma. I am trying to solve a differential equation with
> complex roots. Mathematica is taking the incorrect root at certain points
> when the function crosses over itself. I generated a set of all points at
> which this occurs. The set is
>
> ProblemList={2.8, 5.599, 8.398}
>
> I now want to use these points in a function. My function is
>
> ComplexRoot[t_]:= If[Abs[t - ProblemList[[1]]] > .01 && Abs[t -
> ProblemList[[2]]] > .01 && Abs[t - ProblemList[[ 3]]] > .01,
> Evaluate[I*(2 + 1/2)(I*x[t])^(1 + 1/2)], Evaluate[p'[t - .01]]]
>
> The goal here is to have Mathematica take the correct root for all t other
> than the problem t values, and at those t values simply continue in the
> direction it was heading previously. So I want to then plug into the
> differential equation
>
> solution=NDSolve[{x'[t] == 2p[t], x[0] == 0, p'[t]==ComplexRoot[t], p[0]
> == 1},
> {x, p}, {t,0,10}, WorkingPrecision -> 30, MaxSteps -> Infinity][[1]];
>
> and not get an error. Right now it gives me an error saying that I
> haven't "literally matched the independent variables."
>
> If it works, the following graph should have two loops and look like an
> infinity sign with one of the loops being smaller than the other.
>
> ParametricPlot[{Re[p[t]] /. solution, Im[p[t]] /. solution},
> Evaluate[{t,0,10}],PlotRange -> {{-2, 2}, {-2, 2}}]
>
> What can I do to fix this issue? Any and all help is greatly appreciated.
>
> Thanks,
> Alex
>
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