Open Access

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

Advances in Difference Equations20062006:070325

https://doi.org/10.1155/ADE/2006/70325

Received: 16 September 2004

Accepted: 11 January 2005

Published: 6 February 2006

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.

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Authors’ Affiliations

(1)
Institute of Fundamental Sciences, Massey University

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Copyright

© Boglaev and Hardy 2006

This article is published under license to BioMed Central Ltd. 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.