## International Journal of Differential Equations

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

#### 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 $\delta$ and the perturbation parameter $\epsilon$.

#### Article information

Source
Int. J. Differ. Equ., Volume 2012 (2012), Article ID 572723, 12 pages.

Dates
Accepted: 1 October 2012
First available in Project Euclid: 24 January 2017

https://projecteuclid.org/euclid.ijde/1485226832

Digital Object Identifier
doi:10.1155/2012/572723

Mathematical Reviews number (MathSciNet)
MR2994966

Zentralblatt MATH identifier
1269.34081

#### Citation

File, Gemechis; Reddy, Y. N. Numerical Integration of a Class of Singularly Perturbed Delay Differential Equations with Small Shift. Int. J. Differ. Equ. 2012 (2012), Article ID 572723, 12 pages. doi:10.1155/2012/572723. https://projecteuclid.org/euclid.ijde/1485226832

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