Re: boundary condition for NDSolve
- To: mathgroup at smc.vnet.net
- Subject: [mg45044] Re: [mg45036] boundary condition for NDSolve
- From: CAP F <Ferdinand.Cap at eunet.at>
- Date: Sun, 14 Dec 2003 06:22:41 -0500 (EST)
- References: <200312131106.GAA11110@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Yama Masu wrote:
>
> I would like to solve membrane oscillation between two square shaped fixed boundaries
> with NDSolve.
> D[u[x, y, t], {t, 2}] == D[u[x, y, t], {x, 2}] + D[u[x, y, t], {y, 2}] + f[x, y, t],
> where f is an external force.
>
> The boundary condition for the outside square is given by
> u[x, -1, t] == 0, u[x, 1, t] == 0, u[-1, y, t] == 0, u[1, y, t] == 0.
>
> How can I give the boundary condition for the square inside?
>
> I tried
> If[y>-0.5 && y<0.5, u[0.5, y, t]==0] etc. but this didn't work.
>
> Masu
Hi, Yama Masu :
So far as I see you want to solve an inhomogeneous partial diff equation
for two different boundary conditions, namely two squares
and you want to use NDSolve.
My remarks are :
1.)NDSolve is not well suited to solve part de. It can do this for
very few pde.
2.)Your membrane pde is of elliptic type. Then theory says that for
elliptic pde ONLY ONE boundary can be given except you place a
singularity within the center of the inner boundary domain.
3.)Your problem has been solved and published, see below:
page 263, chapter 5.2, "Boundary problems with two closed boundaries"
Mathematical Methods of Physics and Engineering with Mathematica
Ferdinand F . Cap, CRC-Press/Chapman and Hall, 2003,
ISBN 1584884029, 56 Codes to be downloaded from
www.crcpress.com
The problem of two boundaries is code c46, outer homogeneous boundary on
circle, inner homogeneous boundary on square.
If I can be of any help, please contact me by e mail.F. Cap
- References:
- boundary condition for NDSolve
- From: Yama Masu <yamagomas@yahoo.co.jp>
- boundary condition for NDSolve