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
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.