Advances in Difference Equations
Volume 2006 (2006), Article ID 70325, 38 pages

Monotone finite difference domain decomposition algorithms and applications to nonlinear singularly perturbed reaction-diffusion problems

Igor Boglaev and Matthew Hardy

Institute of Fundamental Sciences, Massey University, Private Bag, Palmerston North 11-222, New Zealand

Received 16 September 2004; Revised 21 December 2004; Accepted 11 January 2005

Copyright © 2006 Igor Boglaev and Matthew Hardy. 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.


This paper deals with monotone finite difference iterative algorithms for solving nonlinear singularly perturbed reaction-diffusion problems of elliptic and parabolic types. Monotone domain decomposition algorithms based on a Schwarz alternating method and on box-domain decomposition are constructed. These monotone algorithms solve only linear discrete systems at each iterative step and converge monotonically to the exact solution of the nonlinear discrete problems. The rate of convergence of the monotone domain decomposition algorithms are estimated. Numerical experiments are presented.