Efficient Iterative Approximation for Nonlinear Porous Medium Equation with Drainage Model

Abstract

The porous medium equation with drainage was applied to model various phenomena in physics and biology fields. The exact solutions of the model are limited, and an efficient numerical approach is demanded to study the model. The main contribution of this research is to develop an iterative approximation that can efficiently solve the porous medium equation with the drainage model. This paper presented a modified successive over-relaxation iterative method derived from using a quarter-sweep implicit finite-difference approximation. Several models of the porous medium equation with drainage are selected to validate the efficiency of the proposed method. The experiment used different sizes of the system of equations to analyse the efficiency of the proposed method. The proposed method is compared against several existing methods, and the results support the superiority of the proposed method in the number of iterations and computer execution time.