A uniformly convergent scheme for a system of reaction–diffusion equations
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摘要
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.
论文关键词:65N12,65N30,65N06,Singular perturbation,Reaction–diffusion problems,Uniform convergence,Coupled system,Shishkin mesh
论文评审过程:Received 21 October 2005, Revised 9 June 2006, Available online 27 July 2006.
论文官网地址:https://doi.org/10.1016/j.cam.2006.06.005