Re: 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: [mg59661] 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: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
- Date: Tue, 16 Aug 2005 05:39:21 -0400 (EDT)
- Organization: Uni Leipzig
- References: <ddpt58$orc$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi, NDSolve[] is for intial-boundary value problems n+1 and not for pure boundary value problems. You can use the tim depend equation and integrate it until the solution does not change any more. Regards Jens "Nasser Abbasi" <nma at 12000.org> schrieb im Newsbeitrag news:ddpt58$orc$1 at smc.vnet.net... | | 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 | | | | | | |