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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 731057, 4 pages
http://dx.doi.org/10.1155/2014/731057
Research Article

Numerical Solution of Singularly Perturbed Delay Differential Equations with Layer Behavior

1Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
2Department of Mathematics and Institute for Mathematical Research, University Putra Malaysia (UPM), 43400 Serdang, Selangor, Malaysia

Received 4 September 2013; Accepted 24 December 2013; Published 16 January 2014

Academic Editor: Aref Jeribi

Copyright © 2014 F. Ghomanjani et al. 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.

Abstract

We present a numerical method to solve boundary value problems (BVPs) for singularly perturbed differential-difference equations with negative shift. In recent papers, the term negative shift has been used for delay. The Bezier curves method can solve boundary value problems for singularly perturbed differential-difference equations. The approximation process is done in two steps. First we divide the time interval, into subintervals; second we approximate the trajectory and control functions in each subinterval by Bezier curves. We have chosen the Bezier curves as piecewise polynomials of degree and determined Bezier curves on any subinterval by control points. The proposed method is simple and computationally advantageous. Several numerical examples are solved using the presented method; we compared the computed result with exact solution and plotted the graphs of the solution of the problems.