On quarter-sweep finite difference scheme for one-dimensional porous medium equations

In this article, we introduce an implicit finite difference approx-imation for one-dimensional porous medium equations using Quarter-Sweep approach. We approximate the solutions of the nonlinear porous medium equa-tions by the application of the Newton method and use the Gauss-Seidel itera-tion. This yields a numerical method that reduces the computational complex-ity when the spatial grid spaces are reduced. The numerical result shows that the proposed method has a smaller number of iterations, a shorter computation time and a good accuracy compared to Newton-Gauss-Seidel and Half-Sweep Newton-Gauss-Seidel methods