Posted by Christian Oehreneder on August 13, 1998 at 12:10:08:
I need to solve a problem of the following kind:
d^2 U(x,y)/dx^2 + d^2 U(x,y)/dy^2 - U(x,y)*f(x,y) = - g(x,y)
or in discretized form
U[m-1,n] + U[m+1,n] + U[m,n-1] + U[m,n+1] - 4*U[m,n] - U[m,n]*f[m,n] = -g[n,m]
f >= 0
The problem is to be solved on a square domain.
At the boundary I use a symmetric continuation of U
to give the above equation meaning.
Is this a "known" problem. If yes, under what name is
it referenced in the literature?
For the 1D case it involves the solution of a tridiagonal
symmetric Matrix with subdiagonal elements all the same.
I solved with some special solver for tridiagonal Matrizes
which works fine.
For the 2D case everything seems more complicated. In view
of the very regular structure of the equation I thought
there might be a special purpose solver for that type
of problems. It seems to be in close relation to other
finite difference problems.
Can anyone give me an advise?