# 2D heat equation using gauss-seidel method

1. Apr 13, 2012

### strythe

Hi guys. Badly need some help. We were given this 2D heat equation BV problem. On the square plate, values on all four edges are given (2 are Neumann, 2 are Dirichlet). And we are to solve this problem using FDM, on a 5point stencil.

So I used FDM approximations to derive the formula for the temperature at the nodes in terms of its adjacent nodes. What I got was a matrix formulation: [Aij][Tj]=[Cj] where A is the coefficient matrix, T --> variables, C --> constants. So I was able to solve for the temperature at the nodes. Then, we have to iterate the whole Gauss Seidel process until a certain %relative error is achieved.

How do I proceed with the iteration after the first one? Since from what I can think of, the first temperature values obtained doesn't change the matrix formulation. Or am I wrong?