Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 912541, 13 pages
Research Article

Solution of the Porous Media Equation by a Compact Finite Difference Method

Department of Mathematics, Faculty of Art and Science, Pamukkale University, 20070 Denizli, Turkey

Received 30 April 2008; Revised 10 October 2008; Accepted 16 January 2009

Academic Editor: Alois Steindl

Copyright © 2009 Murat Sari. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Accurate solutions of the porous media equation that usually occurs in nonlinear problems of heat and mass transfer and in biological systems are obtained using a compact finite difference method in space and a low-storage total variation diminishing third-order Runge-Kutta scheme in time. In the calculation of the numerical derivatives, only a tridiagonal band matrix algorithm is encountered. Therefore, this scheme causes to less accumulation of numerical errors and less use of storage space. The computed results obtained by this way have been compared with the exact solutions to show the accuracy of the method. The approximate solutions to the equation have been computed without transforming the equation and without using linearization. Comparisons indicate that there is a very good agreement between the numerical solutions and the exact solutions in terms of accuracy. This method is seen to be a very good alternative method to some existing techniques for such realistic problems.