Volume 26, Issue 1
A Monotone Domain Decomposition Algorithm for Solving Weighted Average Approximations to Nonlinear Singularly Perturbed Parabolic Problems
DOI:

J. Comp. Math., 26 (2008), pp. 76-97

Published online: 2008-02

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• 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.

• Keywords

Parabolic reaction-diffusion problem Boundary layers $\theta$-method Monotone domain decomposition algorithm Uniform convergence

65M06 65M12 65M55.

TY - JOUR T1 - A Monotone Domain Decomposition Algorithm for Solving Weighted Average Approximations to Nonlinear Singularly Perturbed Parabolic Problems JO - Journal of Computational Mathematics VL - 1 SP - 76 EP - 97 PY - 2008 DA - 2008/02 SN - 26 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8612.html KW - Parabolic reaction-diffusion problem KW - Boundary layers KW - $\theta$-method KW - Monotone domain decomposition algorithm KW - Uniform convergence AB - 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.