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Uniform convergence of a finite difference scheme for a system of coupledreaction‐diffusion equations
Author(s) -
Linss Torsten,
Madden Niall
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310551
Subject(s) - piecewise , mathematics , polygon mesh , perturbation (astronomy) , mathematical analysis , uniform convergence , convergence (economics) , diffusion , scheme (mathematics) , reaction–diffusion system , diffusion equation , finite difference scheme , finite difference method , boundary layer , finite difference , physics , geometry , computer science , mechanics , computer network , economy , bandwidth (computing) , service (business) , quantum mechanics , economics , thermodynamics , economic growth
We study a system of coupled reaction‐diffusion equations. The equations have diffusion parameters of different magnitudes associated with them. Near each boundary, their solution exhibit two overlapping layers. A difference scheme on layer‐adapted piecewise uniform meshes is used to solve the system numerically. We show that the scheme is almost second‐order convergent, uniformly in both perturbation parameters, thus improving previous results [3].