International Journal of Differential Equations

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

Süleyman Cengizci

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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.

Article information

Source
Int. J. Differ. Equ., Volume 2017 (2017), Article ID 7269450, 8 pages.

Dates
Received: 7 April 2016
Accepted: 11 January 2017
First available in Project Euclid: 12 April 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1491962518

Digital Object Identifier
doi:10.1155/2017/7269450

Mathematical Reviews number (MathSciNet)
MR3610992

Zentralblatt MATH identifier
06915940

Citation

Cengizci, Süleyman. An Asymptotic-Numerical Hybrid Method for Solving Singularly Perturbed Linear Delay Differential Equations. Int. J. Differ. Equ. 2017 (2017), Article ID 7269450, 8 pages. doi:10.1155/2017/7269450. https://projecteuclid.org/euclid.ijde/1491962518


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