Laplace's and Poisson's Equations, discretized version

The discretized version reads $$\begin{equation*} u_{xx}\approx \frac{u(x+h,y)-2u(x,y)+u(x-h,y)}{h^2}, \end{equation*}$$ and $$\begin{equation*} u_{yy}\approx \frac{u(x,y+h)-2u(x,y)+u(x,y-h)}{h^2}, \end{equation*}$$ which we rewrite as $$\begin{equation*} u_{xx}\approx \frac{u_{i+1,j}-2u_{i,j}+u_{i-1,j}}{h^2}, \end{equation*}$$ and $$\begin{equation*} u_{yy}\approx \frac{u_{i,j+1}-2u_{i,j}+u_{i,j-1}}{h^2}. \end{equation*}$$

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