$\displaystyle u_{i,j}^{n+1}=\frac{1}{4}[u_{i-1,j}^{n+1}+u_{i,j-1}^{n+1}+u_{i+1,j}^{n}+u_{i,j+1}^{n}-h^{2}f(x_{i},y_{j})] \ \ \ \ \ i=1,..,N-2, \ \ \ \ j=1,...,N-2 $
i am considering how to apply this relaxation.
$\displaystyle u_{i,j}^{n+1}=\frac{1}{4}[u_{i-1,j}^{n+1}+u_{i,j-1}^{n+1}+u_{i+1,j}^{n}+u_{i,j+1}^{n}-h^{2}f(x_{i},y_{j})] \ \ \ \ \ i=1,..,N-2, \ \ \ \ j=1,...,N-2 $
i am considering how to apply this relaxation.