Table of Contents
Advances in Numerical Analysis
Volume 2016, Article ID 8903184, 9 pages
http://dx.doi.org/10.1155/2016/8903184
Research Article

Analysis of Linear Piecewise Constant Delay Systems Using a Hybrid Numerical Scheme

Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 8415683111, Iran

Received 30 April 2016; Accepted 3 July 2016

Academic Editor: Marc Gerritsma

Copyright © 2016 H. R. Marzban and S. M. Hoseini. 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

An efficient computational technique for solving linear delay differential equations with a piecewise constant delay function is presented. The new approach is based on a hybrid of block-pulse functions and Legendre polynomials. A key feature of the proposed framework is the excellent representation of smooth and especially piecewise smooth functions. The operational matrices of delay, derivative, and product corresponding to the mentioned hybrid functions are implemented to transform the original problem into a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the proposed numerical scheme.