Parameter–uniform Fitted Mesh Method for Quasilinear Differential Equations with Boundary Layers

Abstract

AbstractSingularly perturbed quasilinear boundary value problems exhibiting boundary layers are considered. Special piecewise-uniform meshes are constructed which are fitted to these boundary layers. Numerical methods composed of upwind difference operators and these fitted meshes are shown to be parameter robust, in the sense that the solutions satisfy an error estimate in the maximum norm which is independent of the value of the singular perturbation parameter. Numerical results supporting the theory are presented.