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Re: How to specify boundary conditions on all 4 sides of a plate for a steady state heat equation (PDE) using NDSolve? (Laplace equation)

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  • Subject: [mg59766] Re: How to specify boundary conditions on all 4 sides of a plate for a steady state heat equation (PDE) using NDSolve? (Laplace equation)
  • From: "Nasser Abbasi" <nma at 12000.org>
  • Date: Sat, 20 Aug 2005 03:14:05 -0400 (EDT)
  • References: <ddpt58$orc$1@smc.vnet.net> <ddscf6$ai1$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

"Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de> wrote in message 
news:ddscf6$ai1$1 at smc.vnet.net...
>
> Hi,
>
> NDSolve[] is for intial-boundary value problems
> n+1 and not
> for pure boundary value problems.
> You can use the tim depend equation and integrate
> it until the solution
> does not change any more.
>
> Regards
>  Jens

Well, I think I'll go back to using direct numerical/mesh based 
methods.

Those will work for any type of linear PDE (in general), and even if 
one must write more code to do that, one can get more control on what 
is going on, and one does not have the limitations imposed by NDSolve.

For fun, here is the solution to 1-D diffusion PDE using FTCS scheme 
(forward time centered space) using Mathematica code. I just hacked 
this quickly, and would like to go over it to again to make it more of 
a 'functional' style, but I find it hard to avoid using the For loop 
sometimes, but I do use the Table command a lot, so I think the code 
is functional :)

http://12000.org/my_notes/mma_matlab_control/e65/HTML/e65.htm

compare the above to the solution given by using NDSolve shown below 
(much less code ofcourse)

http://12000.org/my_notes/mma_matlab_control/e57/HTML/e57.htm

Next, I'll solve the 2D steady state heat equation (Laplace PDE) using 
such direct method, may be using a different scheme.

btw, I found Mathematica Matrix operations and general performance 
doing this to be really fast, I was surprised, I thought it will be a 
little slower.

Nasser






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