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Title: Numerical solution of time-delay systems by Hermite wavelet

Authors: Akram Kheirabadi; Asadollah Mahmoudzadeh Vaziri; Sohrab Effati

Addresses: Department of Mathematics, Faculty of Mathematical Science and Statistics, University of Birjand, Birjand, 25529, Iran ' Department of Mathematics, Faculty of Mathematical Science and Statistics, University of Birjand, Birjand, 25529, Iran ' Faculty of Mathematical Sciences, Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, 25529, Iran

Abstract: This paper presents a direct numerical method based on Hermite wavelet to find the solution of time delay systems. The operational matrices of integration, differentiation, production, and delay are derived and utilised to reduce the time-delay dynamical system to a set of algebraic equations. Thus, the problem is simplified to a great extent. The method is easy to implement. The illustrative examples with time-invariant and time-varying coefficients demonstrate the validity of the method.

Keywords: TDS; time-delay system; Hermite wavelet; operational matrix; direct method; orthogonal functions.

DOI: 10.1504/IJDSDE.2021.113900

International Journal of Dynamical Systems and Differential Equations, 2021 Vol.11 No.1, pp.1 - 17

Received: 04 Jun 2018
Accepted: 22 Mar 2019

Published online: 21 Mar 2021 *

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