Half-Sweep Approximation for Nonlinear Diffusion Equation In Two-Dimensional Porous Medium

Abstract

This paper investigates the efficacy of the half-sweep approximation to solve the nonlinear diffusion equation in the two- dimensional porous medium. The half-sweep approximation is systematically formulated, and its stability properties are analysed based on its iterative form. The system of equations corresponding to the approximation equation to the two-dimensional nonlinear diffusion equation is solved using the developed half-sweep Newton-Gauss-Seidel algorithm. The numerical experiment uses several initial boundary value problems in natural science to illustrate the efficacy of the proposed approximation. This study finds that the half-sweep approximation is more efficient than the implicit finite difference approximation in numerical computation. The numerical convergence of the approximation is presented to show the potential of the half-sweep approximation to solve different types of nonlinear diffusion equations in a two-dimensional porous medium.