An asymptotic-numerical hybrid method for singularly perturbed system of two-point reaction-diffusion boundary-value problems

Abstract

This article focuses on the numerical approximate solution of singularly perturbed systems of secondorder reaction-diffusion two-point boundary-value problems for ordinary differential equations. To handle these types of problems, a numerical-asymptotic hybrid method has been used. In this hybrid approach, an efficient asymptotic method, the so-called successive complementary expansion method (SCEM) is employed first, and then a numerical method based on finite differences is applied to approximate the solution of corresponding singularly perturbed reactiondiffusion systems. Two illustrative examples are provided to demonstrate the efficiency, robustness, and easy applicability of the present method with convergence properties