A hybrid simulation for a system of singularly perturbed two-point reaction-diffusion equations

Abstract

This study concerns with singularly perturbed systems of second-order reaction-diffusion equations in ODE's. To handle this type of problems, a numerical-asymptotic hybrid method is employed. In this hybrid method, an efficient asymptotic method, the so-called Successive complementary expansion method (SCEM) is applied first and then, a numerical method based on finite differences is proposed to approximate the solution of the corresponding singularly perturbed reaction-diffusion systems. Two illustrative examples are provided to show the efficiency and easy-applicability of the present method with convergence properties.