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

Abstract

This study is concerned with systems of singularly perturbed 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 so-called Successive complementary expansion method (SCEM) is employed first and then, a numerical method based on finite differences is proposed to approximate to the solution of corresponding singularly perturbed reaction-diffusion systems. Two numerical examples are provided to show the efficiency and easy-applicability of the present method with convergence properties.