Document Type : Research Paper

Authors

• Reza Ezzati ¹
• Mostafa Safavi ²
• Amirahmad Khajehnasiri ³
• Akbar Jafari Shaerlar ⁴

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

• Hat basis functions‎
• ‎Delay operational matrix‎
• ‎Delay systems