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boundary condition for NDSolve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg45036] boundary condition for NDSolve
  • From: Yama Masu <yamagomas at yahoo.co.jp>
  • Date: Sat, 13 Dec 2003 06:06:46 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

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


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