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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 493204, 9 pages
http://dx.doi.org/10.1155/2013/493204
Research Article

Exponential Collocation Method for Solutions of Singularly Perturbed Delay Differential Equations

1Department of Mathematics, Faculty of Science, Akdeniz University, Antalya 07058, Turkey
2Department of Mathematics, Faculty of Science, Celal Bayar University, Manisa 45040, Turkey

Received 16 June 2013; Accepted 22 July 2013

Academic Editor: Valery Y. Glizer

Copyright © 2013 Şuayip Yüzbaşı and Mehmet Sezer. 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

This paper deals with the singularly perturbed delay differential equations under boundary conditions. A numerical approximation based on the exponential functions is proposed to solve the singularly perturbed delay differential equations. By aid of the collocation points and the matrix operations, the suggested scheme converts singularly perturbed problem into a matrix equation, and this matrix equation corresponds to a system of linear algebraic equations. Also, an error analysis technique based on the residual function is introduced for the method. Four examples are considered to demonstrate the performance of the proposed scheme, and the results are discussed.