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. >