### Operational matrix and their applications for solving time-varying delay systems

Document Type : Research Paper

Authors

1 Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran

2 Department of Mathematics, University of Texas at Dallas, Richardson, USA

3 Department of Mathematics, North Tehran Branch, Islamic Azad University, Tehran, Iran

4 Department of Mathematics, Khalkhal Branch, Islamic Azad University, Khalkhal, Iran

Abstract

The purpose of this paper is to provide a generalized formulation for Hat basis functions and to present the operational matrices for finding the approximate solution for time-invariant delay systems‎. ‎From this prospect‎, ‎the hat basic functions of integration‎, ‎delay‎, ‎product‎, ‎and dual are derived‎, ‎which are utilized to practically reduce the time-varying delay systems solution to the simplest system of algebraic equations‎. ‎The numerical results compared and tabled with previous works showcase the method's simplicity‎, ‎clarity‎, ‎and effectiveness through the three examples.

Keywords

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###### Volume 14, Issue 9September 2023Pages 79-88
• Receive Date: 24 August 2022
• Revise Date: 14 November 2022
• Accept Date: 26 November 2022