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$$\frac{{\partial }^{2}u}{\partial x^2}+\frac{{\partial }^{2}u}{\partial x^2}=f(x,y)$$

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.

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