Re: 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: [mg59701] Re: [mg59688] 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: Pratik Desai <pdesai1 at umbc.edu>
- Date: Thu, 18 Aug 2005 00:16:33 -0400 (EDT)
- References: <ddpt58$orc$1@smc.vnet.net> <dds9co$91c$1@smc.vnet.net> <200508170800.EAA24887@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Nasser Abbasi wrote: >"James Gilmore" <james.gilmore at yale.edu> wrote in message >news:dds9co$91c$1 at smc.vnet.net... > > > >>This is a classic mathematical physics BVP. You should approach this >>problem >>in Mathematica, as you would by hand: use separation of variables, >>and then >>a fourier expansion to satisfy the boundary conditions. >> >> > >Not if you want to use a numerical solvers such as NDSolve. That is >the whole idea of using NDSolve. > >I know how to solve these by hand, and also by direct numerical >approach, I've solved my of these before and more advanced ones when I >took some courses at the Math dept at UC Berkeley one year ago, I was >just playing around to see if NDSolve can solve BVP and get the same >plots I got when I solved this problem by hand using sepration of >variables. > > > >>There are many books >>that explain how to do this. >> >> > >Yes, and my home library contains many fine books on PDE's. I like the >Satnley Farlow book, and Mary Boas has excellent chapter on the >subject, but a bit short on detailes. Also Richard Haberman applied >PDE's is nice, and if you want to see a nice new book with the cover >showing solutions of PDE's plots which I am sure was made using >Mathematica check Charles MacCluer's BVP and fourier expansions Dover >book, but it does not contain any Mathematica code. Another book which >uses a CAS system to solve PDE's is by David Betounes called PDE's for >computational science, lots of examples and plots. > >Is there a short list somewhere which makes it clear what kind/class >of PDE's Mathematica can solve and not solve directly using NDSolve or >even DSolve? > Would'nt that be awesome? > And why is it that NDSolve can solve an initial value PDE >and not BVP? I wonder if NDSolve will be able to solve a BVP PDE in >next version? > > Have you tried shooting methods, there must be a package doing just that floating around > > > >>"Nasser Abbasi" <nma at 12000.org> wrote in message >>news:ddpt58$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 >>> >>> >>> >>> >>> >>> >>> >>> >>> >> >> >> > > > > Best regards, Pratik Desai -- Pratik Desai Graduate Student UMBC Department of Mechanical Engineering Phone: 410 455 8134
- References:
- 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@12000.org>
- Re: How to specify boundary conditions on all 4 sides of a plate for a steady state heat equation (PDE) using NDSolve? (Laplace equation)