Numerical Solution of Piecewise Constant Delay Systems Based on a Hybrid Framework

H R Marzban,S Hajiabdolrahmani

doi:10.1155/2016/9754906

Abstract

An efficient numerical scheme for solving delay differential equations with a piecewise constant delay function is developed in this paper. The proposed approach is based on a hybrid of block-pulse functions and Taylor’s polynomials. The operational matrix of delay corresponding to the proposed hybrid functions is introduced. The sparsity of this matrix significantly reduces the computation time and memory requirement. The operational matrices of integration, delay, and product are employed to transform the problem under consideration into a system of algebraic equations. It is shown that the developed approach is also applicable to a special class of nonlinear piecewise constant delay differential equations. Several numerical experiments are examined to verify the validity and applicability of the presented technique.

Highlights

Many problems arising in diverse areas of science and engineering can be described by delay differential equations (DDEs)
Many research works have been devoted to the numerical treatments of DDEs involving constant delay [4,5,6,7,8,9,10,11,12,13,14,15,16]
An efficient and flexible framework has been successfully developed for solving piecewise constant delay systems

Summary

Introduction

Many problems arising in diverse areas of science and engineering can be described by delay differential equations (DDEs). Many research works have been devoted to the numerical treatments of DDEs involving constant delay [4,5,6,7,8,9,10,11,12,13,14,15,16]. A few papers have been paid to the numerical investigation of delay differential equations with a piecewise constant delay function [17,18,19,20,21]. The situation becomes more complicated when time-delay is a piecewise constant function

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Results

Conclusion