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: [mg59719] 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: Mike Honeychurch <M.Honeychurch at uq.edu.au>
- Date: Thu, 18 Aug 2005 00:17:42 -0400 (EDT)
- Organization: University of Queensland
- References: <ddpt58$orc$1@smc.vnet.net> <dds9co$91c$1@smc.vnet.net> <dduroq$oih$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
On 17/8/05 6:16 PM, in article dduroq$oih$1 at smc.vnet.net, "Nasser Abbasi" <nma at 12000.org> 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? 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? The NDSolve advanced documentation should be the first place to look for this detailed information. Cheers Mike