NEWTON-SOR ITERATIVE METHOD FOR SOLVING THE TWO-DIMENSIONAL POROUS MEDIUM EQUATION

Authors

  • J. V. L. Chew Faculty of Science and Natural Resources, Universiti Malaysia Sabah, 88400 Kota Kinabalu, Sabah
  • J. Sulaiman Faculty of Science and Natural Resources, Universiti Malaysia Sabah, 88400 Kota Kinabalu, Sabah

DOI:

https://doi.org/10.4314/jfas.v9i6s.30

Keywords:

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

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.

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Published

2017-11-10

Issue

Section

Research Articles