I have the following system of equations for $i,j=1,...,n$:
$u_{i-1,j}+u_{i+1,j}+u_{i,j-1}+u_{i,j+1}-4u_{i,j} = f_{i,j}$
The right hand side $f$ is known, as well as $u_{0,j},u_{n+1,j},u_{i,0},u_{i,n+1}$. Eventually I want to solve for u. I tried to rewrite the problem using matrices, but I failed. Is there any way to restructure it in a compact way? The only option I could think of was using something like $\left(\begin{array}{c} u_{11} \\ . \\ .\\u_{n1}\\u_{12}\\.\\.\\.\\u_{nn}\end{array}\right)$, which seems highly unnatural and impractical. Thanks in advance for your help!