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Re: How do I reformulate my NDSolve program

• To: mathgroup at smc.vnet.net
• Subject: [mg86194] Re: How do I reformulate my NDSolve program
• From: "David Park" <djmpark at comcast.net>
• Date: Wed, 5 Mar 2008 03:41:25 -0500 (EST)
• References: <fqit0i$mdt$1@smc.vnet.net>

Maybe you could post some actual working code? For example, what is i, and
what is the I double dot mu?

--
David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/


"Alex Cloninger" <acloninger at wustl.edu> wrote in message
news:fqit0i$mdt$1 at smc.vnet.net...
> So I am trying to run plots of the following coupled differential
> equations, specifically for epsilon=1/2:
>
> solution = NDSolve[{x'[t] == 2p[t], x[0] == 0,
> p'[t] == i*(2 + =CF=B5)(i*x[t])^(1 + =CF=B5), p[0] == 1}, {x, p}, {t,0,10},
> WorkingPrecision -> 40, MaxSteps ->Infinity][[1]];
>
> I then want to plot the p[t] in the complex plane:
>
> ParametricPlot[{Re[p[t]] /. solution, Im[p[t]] /. solution},
> Evaluate[time],PlotRange -> {{-2, 2}, {-2, 2}}]
>
> The problem with this is that my plot has a sharp change in slope at (1,0)
> (t=5.6 or so).  What should happen is that the line continues past p=1 and
> extends out into a small loop before coming back, crossing over itself,
> and continuing along the larger loop.  I know that the reason the graph
> isn't appearing correct has to do with the fact that I'm raising x[t] to a
> fractional power (epsilon=1/2).  Mathematica isn't realizing that it has
> hit a branch cut and is taking the wrong root.
>
> I have two questions.  1) How would I be able to identify these points of
> discontinuities in slope on a more complicated graph (I want to be able to
> do this for any positive rational epsilon)?  2) How would I go about
> fixing the problem so that Mathematica takes the correct root and
> continues in the correct direction?
>
> Thanks for your help,
> Alex
>
> PS. I have version 5.2, but I have access to a better version if there's
> something in it that would help me.
>