Advances in Difference Equations
Volume 2006 (2006), Article ID 70325, 38 pages
doi:10.1155/ADE/2006/70325

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

Abstract

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.