International Journal of Mathematics and Mathematical Sciences 
Volume 2004 (2004), Issue 17, Pages 881-899
doi:10.1155/S0161171204211218

An efficient approach for solving a class of nonlinear 2D parabolic PDEs

Dongjin Kim1,2 and Wlodek Proskurowski1

 1Department of Mathematics, University of Southern California, Los Angeles 90089-1113, CA, USA
2Department of Mathematics, University of Wyoming, Laramie 82071, WY, USA
Received 15 November 2002

Abstract

We consider a class of nonlinear 2D parabolic equations that allow for an efficient application of an operator splitting technique and a suitable linearization of the discretized problem. We apply our scheme to study the finite extinction phenomenon for the porous-medium equation with strong absorption. A comparison of accuracy and computational efficiency of the resulting algorithms for several test problems is presented.