Accurate solution of a system of coupled singularly perturbed reaction-diffusion equations
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.
scientific article; zbMATH DE number 2113797