Table of Contents Author Guidelines Submit a Manuscript
International Journal of Differential Equations
Volume 2017, Article ID 7269450, 8 pages
https://doi.org/10.1155/2017/7269450
Research Article

An Asymptotic-Numerical Hybrid Method for Solving Singularly Perturbed Linear Delay Differential Equations

Institute of Applied Mathematics, Middle East Technical University, 06800 Ankara, Turkey

Correspondence should be addressed to S├╝leyman Cengizci; rt.ude.utem@namyelus.iczignec

Received 7 April 2016; Accepted 11 January 2017; Published 8 February 2017

Academic Editor: Patricia J. Y. Wong

Copyright © 2017 Süleyman Cengizci. 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

In this work, approximations to the solutions of singularly perturbed second-order linear delay differential equations are studied. We firstly use two-term Taylor series expansion for the delayed convection term and obtain a singularly perturbed ordinary differential equation (ODE). Later, an efficient and simple asymptotic method so called Successive Complementary Expansion Method (SCEM) is employed to obtain a uniformly valid approximation to this corresponding singularly perturbed ODE. As the final step, we employ a numerical procedure to solve the resulting equations that come from SCEM procedure. In order to show efficiency of this numerical-asymptotic hybrid method, we compare the results with exact solutions if possible; if not we compare with the results that are obtained by other reported methods.