Numerical Solution of the One-Dimensional Poisson Problem via Iterative Methods and Sparse Matrices

We present the numerical solution of the one-dimensional Poisson problem using sparse matrix structures and iterative methods. We analyze the performance of the Gauss–Seidel and Successive Over-Relaxation (SOR) methods applied to the resulting linear systems obtained via finite difference discretization. Numerical experiments illustrate the convergence behavior and efficiency of these methods.