A COMPARATIVE STUDY OF A CLASS OF LINEAR AND NONLINEAR PANTOGRAPH DIFFERENTIAL EQUATIONS VIA DIFFERENT ORTHOGONAL POLYNOMIAL WAVELETS

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Published: Jun 30, 2024
DOI: https://doi.org/10.22452/mjs.vol43no2.9
Keywords:
Pantograph differential equation Muntz wavelets Chebyshev wavelets of different kinds Operational matrix Collocation nodes

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Ashish Rayal
Department of Mathematics, School of Applied and Life Sciences, Uttaranchal University, Dehradun, 248007, Uttarakhand, INDIA.
https://orcid.org/0000-0001-8954-6605
Prerak A Patel
Gujarat Power Engineering & Research Institute, Gujarat Technological University, Mehsana, Gujarat, INDIA.
Shailendra Giri
Department of Mathematics, Education Department, Govt of Uttarakhand, Pauri Garhwal-246001, INDIA.
Pawan Joshi
Department of Applied Sciences, Shivalik college of Engineering, Dehradun-248197, INDIA.

Abstract

We propose a wavelet approach on different orthogonal polynomials for solving linear and nonlinear pantograph equations with stretch kind. The pantograph differential equation is a unique proportional delay functional differential equation class. It has been used to deal with numerous physics, mathematics, and engineering applications, such as quantum mechanics, control systems, electrodynamics, and number theory. This scheme is based on constructing the operational matrix for integration via different wavelets with their collocation nodes. This study aims to examine the numerical dynamics of the pantograph equation under stretch kind through different orthogonal polynomial wavelets. Illustrative examples are presented to highlight the flexibility of this scheme, and comparisons are made between the mentioned scheme and other existing schemes using tables and graphs. These numerical results correctly predict the applicability and effectiveness of the mentioned scheme.

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How to Cite
Rayal, A. ., Prerak A Patel, Shailendra Giri, & Pawan Joshi. (2024). A COMPARATIVE STUDY OF A CLASS OF LINEAR AND NONLINEAR PANTOGRAPH DIFFERENTIAL EQUATIONS VIA DIFFERENT ORTHOGONAL POLYNOMIAL WAVELETS. Malaysian Journal of Science, 43(2), 75–95. https://doi.org/10.22452/mjs.vol43no2.9
Issue
Vol 43 No 2 (2024): June 2024
Section
Original Articles

Licensee MJS, Universiti Malaya, Malaysia. This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

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