A Monotone Domain Decomposition Algorithm for Solving Weighted Average Approximations to Nonlinear Singularly Perturbed Parabolic Problems

A Monotone Domain Decomposition Algorithm for Solving Weighted Average Approximations to Nonlinear Singularly Perturbed Parabolic Problems

Year:    2008

Journal of Computational Mathematics, Vol. 26 (2008), Iss. 1 : pp. 76–97

Abstract

This paper presents and analyzes a monotone domain decomposition algorithm for solving nonlinear singularly perturbed reaction-diffusion problems of parabolic type. To solve the nonlinear weighted average finite difference scheme for the partial differential equation, we construct a monotone domain decomposition algorithm based on a Schwarz alternating method and a box-domain decomposition. This algorithm needs only to solve linear discrete systems at each iterative step and converges monotonically to the exact solution of the nonlinear discrete problem. The rate of convergence of the monotone domain decomposition algorithm is estimated. Numerical experiments are presented.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2008-JCM-8612

Journal of Computational Mathematics, Vol. 26 (2008), Iss. 1 : pp. 76–97

Published online:    2008-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:    Parabolic reaction-diffusion problem Boundary layers $θ$-method Monotone domain decomposition algorithm Uniform convergence.