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

Authors

SÜLEYMAN CENGİZCİ
SRINIVASAN NATESAN
MEHMET TARIK ATAY

DOI

10.3906/mat-1807-195

Abstract

This article focuses on the numerical approximate solution of singularly perturbed systems of second-order 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 reaction-diffusion systems. Two illustrative examples are provided to demonstrate the efficiency, robustness, and easy applicability of the present method with convergence properties.

Keywords

Singular perturbation problems, reaction-diffusion equations, asymptotic approximations, boundary layers, finite difference method

First Page

460

Last Page

472

Recommended Citation

CENGİZCİ, SÜLEYMAN; NATESAN, SRINIVASAN; and ATAY, MEHMET TARIK (2019) "An asymptotic-numerical hybrid method for singularly perturbed system of two-point reaction-diffusion boundary-value problems," Turkish Journal of Mathematics: Vol. 43: No. 1, Article 37. https://doi.org/10.3906/mat-1807-195
Available at: https://journals.tubitak.gov.tr/math/vol43/iss1/37