How to specify boundary conditions on all 4 sides of a plate for a steady state heat equation (PDE) using NDSolve? (Laplace equation)
- To: mathgroup at smc.vnet.net
- 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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- 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: Curtis Osterhoudt <gardyloo@mail.wsu.edu>
- Re: How to specify boundary conditions on all 4 sides of a plate for a steady state heat equation (PDE) using NDSolve? (Laplace equation)