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Scheme for solving Laplace's (Poisson's) equation

We rewrite Eq. (18) \begin{equation} \tag{19} 4u_{i,j}= \left[u_{i,j+1}+u_{i,j-1}+u_{i+1,j}+u_{i-1,j}\right] -h^2\rho_{i,j}=\Delta_{ij}-\tilde{\rho}_{ij}, \end{equation} where we have defined \begin{equation*} \Delta_{ij}= \left[u_{i,j+1}+u_{i,j-1}+u_{i+1,j}+u_{i-1,j}\right], \end{equation*} and \begin{equation*} \tilde{\rho}_{ij}=h^2\rho_{i,j}. \end{equation*}