Báo Cáo Báo cáo hóa học MONOTONE FINITE DIFFERENCE DOMAIN DECOMPOSITION ALGORITHMS AND APPLICATIONS TO NONLI

MONOTONE FINITE DIFFERENCE DOMAIN DECOMPOSITION ALGORITHMS AND APPLICATIONS TO NONLINEAR SINGULARLY PERTURBED REACTION-DIFFUSION PROBLEMS IGOR BOGLAEV AND MATTHEW HARDY Received 16 September 2004; Revised 21 December 2004; Accepted 11 January 2005

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. Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.

1. Introduction

We are interested in monotone discrete Schwarz alternating