A parameter-uniform Schwarz method for a coupled system of reaction-diffusion equations

Authors:
Meghan Stephens;Niall Madden
Affiliations:
Department of Mathematics, National University of Ireland, Galway, Ireland;Department of Mathematics, National University of Ireland, Galway, Ireland
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 6
Cited 3

Mesh approximation of singularly perturbed boundary-value problems for systems of elliptic and parabolic equations

Computational Mathematics and Mathematical Physics
Domain decomposition in boundary layers for singularly perturbed problems

Applied Numerical Mathematics - Auckl numerical ordinary differential equations (ANODE 98 workshop)
A second-order parameter-uniform overlapping Schwarz method for reaction-diffusion problems with boundary layers

Journal of Computational and Applied Mathematics
A numerical method for a system of singularly perturbed reaction-diffusion equations

Journal of Computational and Applied Mathematics
Accurate Solution of a System of Coupled Singularly Perturbed Reaction-diffusion Equations

Computing
A uniformly convergent scheme for a system of reaction-diffusion equations

Journal of Computational and Applied Mathematics

An almost fourth order uniformly convergent domain decomposition method for a coupled system of singularly perturbed reaction-diffusion equations

Journal of Computational and Applied Mathematics
A robust overlapping Schwarz domain decomposition algorithm for time-dependent singularly perturbed reaction-diffusion problems

Journal of Computational and Applied Mathematics
Uniformly convergent additive finite difference schemes for singularly perturbed parabolic reaction-diffusion systems

Computers & Mathematics with Applications

Quantified Score

Hi-index	7.29

Visualization

Abstract

We consider an arbitrarily sized coupled system of one-dimensional reaction-diffusion problems that are singularly perturbed in nature. We describe an algorithm that uses a discrete Schwarz method on three overlapping subdomains, extending the method in [H. MacMullen, J.J.H. Miller, E. O'Riordan, G.I. Shishkin, A second-order parameter-uniform overlapping Schwarz method for reaction-diffusion problems with boundary layers, J. Comput. Appl. Math. 130 (2001) 231-244] to a coupled system. On each subdomain we use a standard finite difference operator on a uniform mesh. We prove that when appropriate subdomains are used the method produces @e-uniform results. Furthermore we improve upon the analysis of the above-mentioned reference to show that, for small @e, just one iteration is required to achieve the expected accuracy.