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