Computational method for a nonlinear system of two-parameter singular perturbation problems modeling reaction-convection-diffusion processes

This article aims at the construction and analysis of a computational method for a system of two-parameter singularly perturbed second-order nonlinear differential equations with prescribed boundary conditions modeling reaction-convection-diffusion processes. A fitted mesh method consists of a classical finite difference scheme together with a Shishkin mesh constructed to solve the system. The fitted mesh method is proved to be convergent essentially first-order uniformly with respect to the perturbation parameters. An algorithm using the continuation method is designed to compute the numerical approximations. Numerical experiments support the theoretical results. Since there is no literature on systems of two-parameter singularly perturbed nonlinear differential equations, the present study reveals the characteristics of such systems and contributes to their numerical solution.