×

zbMATH — the first resource for mathematics

A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction-diffusion problems. (English) Zbl 1048.65076
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.

MSC:
65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34E15 Singular perturbations, general theory 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
PDF BibTeX XML Cite
Full Text: DOI