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2014 Numerical Solution of Singularly Perturbed Delay Differential Equations with Layer Behavior
F. Ghomanjani, A. Kılıçman, F. Akhavan Ghassabzade
Abstr. Appl. Anal. 2014: 1-4 (2014). DOI: 10.1155/2014/731057

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.

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F. Ghomanjani. A. Kılıçman. F. Akhavan Ghassabzade. "Numerical Solution of Singularly Perturbed Delay Differential Equations with Layer Behavior." Abstr. Appl. Anal. 2014 1 - 4, 2014. https://doi.org/10.1155/2014/731057

Information

Published: 2014
First available in Project Euclid: 26 March 2014

zbMATH: 07022967
MathSciNet: MR3166649
Digital Object Identifier: 10.1155/2014/731057

Rights: Copyright © 2014 Hindawi

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