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

Authors:
J. L. Gracia;F. J. Lisbona
Affiliations:
Department of Applied Mathematics, University of Zaragoza, Spain;Department of Applied Mathematics, University of Zaragoza, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 4
Cited 5

A uniformly accurate finite-element method for a singularly perturbed one-dimensional reaction-diffusion

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

Computational Mathematics and Mathematical Physics
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 parameter-uniform Schwarz method for a coupled system of reaction-diffusion equations

Journal of Computational and Applied Mathematics
An almost third order finite difference scheme for singularly perturbed reaction-diffusion systems

Journal of Computational and Applied Mathematics
A second-order hybrid finite difference scheme for a system of singularly perturbed initial value problems

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	7.30

Visualization

Abstract

In this work a system of two parabolic singularly perturbed equations of reaction-diffusion type is considered. The asymptotic behaviour of the solution and its partial derivatives is given. A decomposition of the solution in its regular and singular parts has been used for the asymptotic analysis of the spatial derivatives. To approximate the solution we consider the implicit Euler method for time stepping and the central difference scheme for spatial discretization on a special piecewise uniform Shishkin mesh. We prove that this scheme is uniformly convergent, with respect to the diffusion parameters, having first-order convergence in time and almost second-order convergence in space, in the discrete maximum norm. Numerical experiments illustrate the order of convergence proved theoretically.