Advances in Difference Equations
Volume 2010 (2010), Article ID 102484, 13 pages
Research Article

Uniform Second-Order Difference Method for a Singularly Perturbed Three-Point Boundary Value Problem

Department of Mathematics, Faculty of Sciences, Yüzüncü Yil University, 65080 Van, Turkey

Received 21 June 2010; Accepted 15 October 2010

Academic Editor: Paul Eloe

Copyright © 2010 Musa Çakır. 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.


We consider a singularly perturbed one-dimensional convection-diffusion three-point boundary value problem with zeroth-order reduced equation. The monotone operator is combined with the piecewise uniform Shishkin-type meshes. We show that the scheme is second-order convergent, in the discrete maximum norm, independently of the perturbation parameter except for a logarithmic factor. Numerical examples support the theoretical results.