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International Journal of Differential Equations
Volume 2012 (2012), Article ID 572723, 12 pages
http://dx.doi.org/10.1155/2012/572723
Research Article

Numerical Integration of a Class of Singularly Perturbed Delay Differential Equations with Small Shift

Department of Mathematics, National Institute of Technology, Warangal 506 004, India

Received 22 May 2012; Accepted 1 October 2012

Academic Editor: Samir H. Saker

Copyright © 2012 Gemechis File and Y. N. Reddy. 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 have presented a numerical integration method to solve a class of singularly perturbed delay differential equations with small shift. First, we have replaced the second-order singularly perturbed delay differential equation by an asymptotically equivalent first-order delay differential equation. Then, Simpson’s rule and linear interpolation are employed to get the three-term recurrence relation which is solved easily by discrete invariant imbedding algorithm. The method is demonstrated by implementing it on several linear and nonlinear model examples by taking various values for the delay parameter and the perturbation parameter .