A Numerical Method for a Singularly Perturbed Three-Point Boundary Value Problem

Çakır M., Amiraliyev G. M.

JOURNAL OF APPLIED MATHEMATICS, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume:
  • Publication Date: 2010
  • Doi Number: 10.1155/2010/495184
  • Journal Name: JOURNAL OF APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

The purpose of this paper is to present a uniform finite difference method for numerical solution of nonlinear singularly perturbed convection-diffusion problem with nonlocal and third type boundary conditions. The numerical method is constructed on piecewise uniform Shishkin type mesh. The method is shown to be convergent, uniformly in the diffusion parameter epsilon, of first order in the discrete maximum norm. Some numerical experiments illustrate in practice the result of convergence proved theoretically.