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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: [mg59645] 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: Mon, 15 Aug 2005 06:50:36 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

 
hi;

just for fun, I am trying to solve a steady state heat equation i.e. 
laplace equation, for a rectangular plate.

So, I have 4 boundary conditions, one for each side of the plate.

But when I do that, NDSolve says that it is designed to solve initial 
conditions problems only? is this really the case? May be I am not 
defining the B.C. correctly for Mathematica?

The code is below, also I've posted it on my web page with the full 
error message.

http://12000.org/my_notes/mma_matlab_control/e61/HTML/e61.htm

I find the error strange, saying that NDSolve can only solve IC PDE, 
because I solved 1-D heat equation using IC and BC earlier with no 
problem, see this

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

So, I have a feeling that NDSolve can do this, I must be just doing 
something not right.


Remove["Global`*"];
h = 30; w = 10; temp = 100;
eq = D[T[x, y], x, x] + D[T[x, y], y, y] == 0;
bc = {T[0, y] == 0, T[w, y] == 0, T[x, 0] == temp,T[x, h] == 0};
sol = NDSolve[{eq, bc}, T[x, y], {x, 0, w}, {y, 0, h}]


"Boundary values may only be specified for one independent
variable. Initial values may only be specified at one value of the 
other independent variable."

Nasser








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