@inproceedings{eed6a265b31441a0913aa0134f7575f4,
title = "Chebyshev Collocation Method for Pantograph Delay Differential Equations with Linear Functional Arguments",
abstract = "Pantograph equations are fundamental models of delay differential equations that are used to model a variety of physical and engineering phenomena. This manuscript presents a numerical scheme using Chebyshev collocation for solving general pantograph equations with variable coefficients and linear functional arguments. Nonlinear pantograph differential equations are transformed into nonlinear algebraic equations which provide matrix representations. A numerical algorithm is used to solve nonlinear algebraic equations in their unknowns. Using residual functions, we developed a method for analyzing errors in the proposed scheme. It is shown that the proposed method is accurate and effective for Pantograph equations. We provide numerical examples of linear and nonlinear problems to confirm the effectiveness and reliability of the proposed method.",
keywords = "Chebyshev polynomials, Collocation points, Pantograph delay differential equation, Proportional delay",
author = "Rihan, \{Fathalla A.\} and Ola Mohamed",
note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.; International Symposium on Mathematical Analysis of Fractals and Dynamical Systems, ISMAFDS 2023 ; Conference date: 24-08-2023 Through 25-08-2023",
year = "2025",
doi = "10.1007/978-3-031-58641-5\_16",
language = "English",
isbn = "9783031586408",
series = "Springer Proceedings in Physics",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "233--251",
editor = "Santo Banerjee and A. Gowrisankar and D. Easwaramoorthy and S. Nandhini and A. Manimaran",
booktitle = "Interplay of Fractals and Complexity in Mathematical Modelling and Physical Patterns - Selected Proceedings of the International Symposium on Mathematical Analysis of Fractals and Dynamical Systems, ISMAFDS 2023",
}