A UNIFORMLY CONVERGENT METHOD FOR A LINEAR SINGULARLY-PERTURBED REACTION-DIFFUSION PROBLEM ON A LISEIKIN TYPE OF MESH

Abstract

In this paper, we consider the numerical solution of a linear singularly perturbed reaction-diffusion boundary value problem, where a small perturbation parameter multiplies the second-order derivative. To achieve this, we approximate the differential equation using a central difference scheme on a Liseikin-type mesh. Furthermore, it is shown that the proposed method is uniformly convergent with respect to the perturbation parameter with an order of convergence of 2. Finally, we provide two numerical examples that illustrate the theoretical results regarding the uniform convergence of the discrete problem, as well as the robustness of the method.