The difference schemes for solving singularly perturbed three-point boundary value problem

Çakır M., Çimen E., Amiraliyev G. M.

LITHUANIAN MATHEMATICAL JOURNAL, vol.60, no.2, pp.147-160, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 60 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.1007/s10986-020-09471-z
  • Journal Name: LITHUANIAN MATHEMATICAL JOURNAL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH, DIALNET
  • Page Numbers: pp.147-160
  • Keywords: boundary value problem, exponentially fitted difference scheme, nonlocal condition, singular perturbation, uniformly convergence
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In this paper, we propose and analyze numerical treatment for a singularly perturbed convection-diffusion boundary value problem with nonlocal condition. First, the boundary layer behavior of the exact solution and its first derivative have been estimated. Then we construct a finite difference scheme on a uniform mesh. We prove the uniform convergence of the proposed difference scheme and give an error estimate. We also present numerical examples, which demonstrate computational efficiency of the proposed method.