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Re: Help me : Solve a simple PDE in Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg110532] Re: Help me : Solve a simple PDE in Mathematica
• From: schochet123 <schochet123 at gmail.com>
• Date: Wed, 23 Jun 2010 01:54:17 -0400 (EDT)
• References: <hvmvoo$pp1$1@smc.vnet.net> <hvn9ms$7iv$1@smc.vnet.net>

Please note the recent message with Subject:  Help me : Solve a simple
PDE in Mathematica
by Oliver Ruebenkoenig from Wolfram
who points out his Package available at
http://library.wolfram.com/infocenter/Conferences/7549/

It uses a finite element method to discretize multi-dimensional pure
boundary value problems and then solves the resulting system of linear
equations

This will probably solve your problem.

It can also solve time-dependent problems by using NDSolve on the
discretized system.

Very nice job, Oliver

Steve

On Jun 22, 2:02 pm, thaihang le <thaihang... at gmail.com> wrote:
> Dear Steve,
>
> Thank you for your great help.
>
> With your answer, no i understand. Solving PDE is not as simple
> although we know the equation and boundary. The most important is how
> to imply it in Mathematica.
>
> Mathematica uses Method of lines and solve very well simple PDE. But
> as my problem, the boundary condition is split in two domains :
>
> At z= 0 :
> When r < 1 : The dirichlet boundary is used : u[r,z] =0
> When r > 1 : the Neumann is used : D[u[r,z],{r,1}] = 0
>
> That's why i dont know how to imply this in Mathematica. For example,
> if the boundary is the same like this :
>
> r < 1 : u[r,z]=0
> r> 1 : u[r,z] =1
>
> I can imply in Mathematica as : z=0 :  u[r,0] == If[r > 1, 1, 0].
>
> Thanks again Steve.
> I try to go by another approach.