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Mathematical Problems in Engineering
Volume 2014, Article ID 602641, 16 pages
http://dx.doi.org/10.1155/2014/602641
Research Article

Bezier Curves Based Numerical Solutions of Delay Systems with Inverse Time

1Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
2Department of Mathematics, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
3Department of Control, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

Received 10 July 2013; Accepted 29 December 2013; Published 27 February 2014

Academic Editor: Mufid Abudiab

Copyright © 2014 F. Ghomanjani et al. 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

This paper applied, for the first time, the Bernstein’s approximation on delay differential equations and delay systems with inverse delay that models these problems. The direct algorithm is given for solving this problem. The delay function and inverse time function are expanded by the Bézier curves. The Bézier curves are chosen as piecewise polynomials of degree , and the Bézier curves are determined on any subinterval by control points. The approximated solution of delay systems containing inverse time is derived. To validate accuracy of the present algorithm, some examples are solved.