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Journal of Applied Mathematics
Volume 2010, Article ID 495184, 17 pages
Research Article

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

1Department of Mathematics, Faculty of Sciences, 100. Y. University, 65080 Van, Turkey
2Department of Mathematics, Faculty of Sciences, Sinop University, 57000 Sinop, Turkey

Received 30 October 2009; Accepted 13 April 2010

Academic Editor: Michela Redivo-Zaglia

Copyright © 2010 Musa Çakır and Gabil M. Amiraliyev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 ε, of first order in the discrete maximum norm. Some numerical experiments illustrate in practice the result of convergence proved theoretically.