Accurate solution of a system of coupled singularly perturbed reaction-diffusion equations
type: Item
instance of: scholarly article
title: Accurate solution of a system of coupled singularly perturbed reaction-diffusion equations
zbMATH Open document ID: 1057.65046
published in: Computing
publication date: 2004-11-05T00:00:00Z
review text: This paper deals with the boundary value problem for systems of two coupled singularly perturbed reaction-diffusion equations with small constants \(\varepsilon\), \(\mu\) in \((0,1]\). The authors extend the results of \textit{N. Madden} and \textit{M. Stynes} [IMA J. Numer. Anal. 23, No. 4, 627--644 (2003; Zbl 1048.65076)] by proving that for \(0< \varepsilon\leq\mu\ll 1\) a finite difference method on a Shishkin mesh gives second-order rate of convergence. The results of a numerical experiment in order to verify the conclusions of this paper with a new parameter \(\nu\) are presented.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L50
zbMATH DE Number: 2113797
zbMATH Keywords: system
zbMATH Keywords: reaction-diffusion equations
zbMATH Keywords: finite difference method
zbMATH Keywords: Shishkin mesh
zbMATH Keywords: convergence
zbMATH Keywords: numerical experiment
zbMATH Keywords: singular perturbation
author: Torsten Linss
author: Niall Madden
reviewed by: Pavol Chocholatý
MaRDI profile type: Publication
full work available at URL: s00607-004-0065-3
OpenAlex ID: W2013129667
DOI: 10.1007/S00607-004-0065-3
description: scientific article; zbMATH DE number 2113797