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.