Cauchy problem PDE NDSolve

*To*: mathgroup at smc.vnet.net*Subject*: [mg31002] Cauchy problem PDE NDSolve*From*: "Eugene" <evs at po.cwru.edu>*Date*: Mon, 1 Oct 2001 02:44:27 -0400 (EDT)*Organization*: CWRU*Sender*: owner-wri-mathgroup at wolfram.com

I am trying to solve a parabolic PDE of a Fokker-Plank type that describes time evolution of a Gaussian peak in infinite space with NDSolve (Math 3.0). Obviously, infinite space is the problem, and NDSolve generates something weird. I played with the NDSolve parameters and various transformations, but it didn't help (though the equation coefficients are good smooth functions). Does anybody know a Mathematica program/package for a Cauchy parabolic (diffusion-type) PDE problem in infinite space (asymptotically vanishing boundary conditions)? I hope it should exist because NDSolve in the present form fails to solve even a textbook problem of the diffusion evolution of a Gaussian peak if the diffusion coefficient changes slightly in space (it generates some mesh-dependent crap). Thanks! Eugene