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


Çakır M. , Çimen E. , Amiraliyev G. M.

LITHUANIAN MATHEMATICAL JOURNAL, 2020 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume:
  • Publication Date: 2020
  • Doi Number: 10.1007/s10986-020-09471-z
  • Title of Journal : LITHUANIAN MATHEMATICAL JOURNAL

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.