Madden, Niall; Stynes, Martin A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction-diffusion problems. (English) Zbl 1048.65076 IMA J. Numer. Anal. 23, No. 4, 627-644 (2003). The authors obtain some bounds on the derivatives of the solution of a system of two singularly perturbed reaction-diffusion equations. To derive them the solution is split into a sum of two overlapping layers. The structure of the layers is analyzed and this leads to the construction of a piecewise-uniform mesh that is a variant of the Shishkin mesh. The bounds are used in the convergence analysis of a difference scheme used to solve the problem numerically. Numerical results are presented for a test problem. Reviewer: Dana Petcu (Timişoara) Cited in 2 ReviewsCited in 71 Documents MSC: 65L10 Numerical solution of boundary value problems involving ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations 34E15 Singular perturbations for ordinary differential equations 65L20 Stability and convergence of numerical methods for ordinary differential equations 65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations 65L70 Error bounds for numerical methods for ordinary differential equations Keywords:reaction-diffusion problems; singular perturbation; finite difference method; error bounds; Shishkin mesh; numerical results; convergence × Cite Format Result Cite Review PDF Full Text: DOI Link