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 >