Branch Cuts and NDSolve

*To*: mathgroup at smc.vnet.net*Subject*: [mg85862] Branch Cuts and NDSolve*From*: Alex Cloninger <acloninger at wustl.edu>*Date*: Mon, 25 Feb 2008 07:39:49 -0500 (EST)

So I need to teach Mathematica how to take a root of a complex number. The problem is that the way it does it in NDSolve (for a square root) is just to assume you want the first of the two possible solutions (ie. Sqrt[i]=Exp[i*Pi/4] and not Exp[5i*Pi/4]). I need to teach Mathematica to know which root to take by telling it to continue on the same trajectory that the solution was traveling previously. I'm not sure how to go about that? Basically, some of the complex differential equations I'm trying to solve should tie themselves in a knot, but that doesn't happen without Mathematica knowing which root to take. Is there any way someone could help me out with this problem? I'm not sure how to get started. Thanks, Alex