I'm trying to solve the 2-D Poisson Equation using both Gaussian Elimination (forward elimination and back substitution) and Gauss Seidel method.
The equation is as follows:
$\ d^2u/dx^2 + d^2u/dy^2 = F(x,y)$
After discretization and applying Dirichlet boundaries for y=start and y=end and applying Neumann boundaries for x=start and x=end I ended up with a pentadiagonal coefficient matrix and a right hand side vector that is made up of F and the boundaries (only in the first and last terms of F). The following are images of the coefficient matrix, A, and the right hand side vector F:
I have solved tridiagonal systems using both Gaussian Elimination and Gauss Seidel but I cannot figure out how I would go about doing this for this new pentadiagonal system,
$\ Au=F$ .
Thanks in advance for your help!
P.S. I am writing the code in MATLAB if anyone was interested.