A parameter robust second order numerical method for a singularly perturbed two-parameter problem

In this paper a second order monotone numerical method is constructed for a singularly perturbed ordinary differential equation with two small parameters affecting the convection and diffusion terms. The monotone operator is combined with a piecewise-uniform Shishkin mesh. An asymptotic error bound in the maximum norm is established theoretically whose error constants are shown to be independent of both singular perturbation parameters. Numerical results are presented which support the theoretical results.