A second order numerical method for singularly perturbed problem with non-local boundary condition

Çakır M., AMİRALİ G.

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, vol.67, no.1-2, pp.919-936, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 67 Issue: 1-2
  • Publication Date: 2021
  • Doi Number: 10.1007/s12190-021-01506-z
  • Journal Name: JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, ABI/INFORM, Aerospace Database, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.919-936
  • Keywords: Exponentially fitted difference scheme, Nonlocal condition, Second-order accuracy, Singular perturbation, Uniformly convergence
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

The aim of this paper is to present a monotone numerical method on uniform mesh for solving singularly perturbed three-point reaction-diffusion boundary value problems. Firstly, properties of the exact solution are analyzed. Difference schemes are established by the method of the integral identities with the appropriate quadrature rules with remainder terms in integral form. It is then proved that the method is second-order uniformly convergent with respect to singular perturbation parameter, in discrete maximum norm. Finally, one numerical example is presented to demonstrate the efficiency of the proposed method.