ENHANCED QUARTER-SWEEP ITERATIVE METHOD USING EGS OR FOR SOLVING ONE-DIMENSIONAL POROUS MEDIUM EQUATION

The porous medium equation has various applications in fluid flow, heat transfer, diffusion, and population dynamics. Solving this equation numerically poses significant challenges, particularly when dealing with strong nonlinearities. In this paper, we propose an enhanced quarter-sweep iterative method using the explicit group successive over-relaxation technique. The implicit finite difference method and Newton’s method are applied to form the approximation equation and efficiently solve the system of equations at each time step. The main contribution of this study is the modification of the conventional implicit finite difference scheme into a quarter-sweep finite difference scheme and then the derivation of an explicit group successive over-relaxation solver. The efficiency of the proposed numerical method is demonstrated through comparisons with existing finite difference schemes that use Gauss-Seidel, successive over-relaxation, and explicit group methods as their solver. Numerical experiments are conducted using various grid sizes to ensure the consistency of the numerical solutions. The comparative analysis demonstrates the superiority of the proposed method over existing methods in terms of computational efficiency.