Newton-sor iterative method for solving the two-dimensional porous medium equation

Abstract

In this paper, we consider the application of the Newton-SOR iterative method in obtaining
the approximate solution of the two-dimensional porous medium equation (2D PME). The
nonlinear finite difference approximation equation to the 2D PME is derived by using the
implicit finite difference scheme. The developed nonlinear system is linearized by using the
Newton method. At each temporal step, the corresponding linear systems are solved by using
SOR iteration. We investigate the efficiency of the Newton-SOR iterative method by solving
three examples of 2D PME and the performance is compared with the Newton-GS iterative
method. Numerical results show that the Newton-SOR iterative method is better than the
Newton-GS iterative method in terms of a number of iterations, computer time and maximum absolute errors.

Keywords: porous medium equation; finite difference scheme; Newton; Successive Over
Relaxation, Gauss-Seidel.