\[ \frac{\partial ^2 u}{\partial x^2} + \frac{\partial ^2 u}{\partial x^2} = f(x,y) \]
When solving the above equation using finite difference method on square, in order to make it easy to see the internal structure of the A matrix using the standard 5 points Laplacian scheme, the following is a small function which generates the symbolic format of these equations for a given \(N\), the number of grid points on one edge. At the end of this note, the system equations are generated for \(N=4,5,6,7,8\). One can see the form of the \(A\) matrix with the dominant diagonal.