## Abstract and Applied Analysis

- Abstr. Appl. Anal.
- Volume 2014 (2014), Article ID 731057, 4 pages.

### Numerical Solution of Singularly Perturbed Delay Differential Equations with Layer Behavior

F. Ghomanjani, A. Kılıçman, and F. Akhavan Ghassabzade

#### Abstract

We present a numerical method to solve boundary value problems (BVPs) for singularly perturbed differential-difference equations with negative shift. In recent papers, the term negative shift has been used for delay. The Bezier curves method can solve boundary value problems for singularly perturbed differential-difference equations. The approximation process is done in two steps. First we divide the time interval, into $k$ subintervals; second we approximate the trajectory and control functions in each subinterval by Bezier curves. We have chosen the Bezier curves as piecewise polynomials of degree $n$ and determined Bezier curves on any subinterval by $n+1$ control points. The proposed method is simple and computationally advantageous. Several numerical examples are solved using the presented method; we compared the computed result with exact solution and plotted the graphs of the solution of the problems.

#### Article information

**Source**

Abstr. Appl. Anal., Volume 2014 (2014), Article ID 731057, 4 pages.

**Dates**

First available in Project Euclid: 26 March 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.aaa/1395858527

**Digital Object Identifier**

doi:10.1155/2014/731057

**Mathematical Reviews number (MathSciNet)**

MR3166649

**Zentralblatt MATH identifier**

07022967

#### Citation

Ghomanjani, F.; Kılıçman, A.; Akhavan Ghassabzade, F. Numerical Solution of Singularly Perturbed Delay Differential Equations with Layer Behavior. Abstr. Appl. Anal. 2014 (2014), Article ID 731057, 4 pages. doi:10.1155/2014/731057. https://projecteuclid.org/euclid.aaa/1395858527