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

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 hybr...

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Bibliographic Details
Published inInternational Journal of Differential Equations Vol. 2016; no. 2016; pp. 385 - 395
Main Authors Marzban, Hamid Reza, Hajiabdolrahmani, S.
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Limiteds 01.01.2016
Hindawi Publishing Corporation
John Wiley & Sons, Inc
Hindawi Limited
Wiley
Subjects
Algebra
Constants
Delay
Delay equations
Differential equations
Investigations
Mathematical analysis
Mathematical models
Mathematical research
Numerical analysis
Polynomials
Transforms
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Summary: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.
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ISSN:1687-9643
1687-9651
DOI:10.1155/2016/9754906