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


Cengizci S., Natesan S., Atay M. T.

TURKISH JOURNAL OF MATHEMATICS, vol.43, no.1, pp.460-472, 2019 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 1
  • Publication Date: 2019
  • Doi Number: 10.3906/mat-1807-195
  • Title of Journal : TURKISH JOURNAL OF MATHEMATICS
  • Page Numbers: pp.460-472

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.