Open Access

ARTICLE

Particle Swarm Optimization for Solving Sine-Gordan Equation

Geeta Arora¹, Pinkey Chauhan², Muhammad Imran Asjad³, Varun Joshi¹, Homan Emadifar⁴, Fahd Jarad^5,6,7,*

1 Lovely Professional University, Punjab, 144118, India
2 Jaypee Institute of Information Technology, Noida, 201304, India
3 Department of Mathematics, University of Management and Technology, Lahore, 54770, Pakistan
4 Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran
5 Department of Mathematics, Cankaya University, Etimesgut, Ankara, 06790, Turkey
6 Department of Mathematics, King Abdulaziz University, Saudi Arabia
7 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

* Corresponding Author: Fahd Jarad. Email:

Computer Systems Science and Engineering 2023, 45(3), 2647-2658. https://doi.org/10.32604/csse.2023.032404

Received 17 May 2022; Accepted 14 July 2022; Issue published 21 December 2022

Abstract

The term ‘optimization’ refers to the process of maximizing the beneficial attributes of a mathematical function or system while minimizing the unfavorable ones. The majority of real-world situations can be modelled as an optimization problem. The complex nature of models restricts traditional optimization techniques to obtain a global optimal solution and paves the path for global optimization methods. Particle Swarm Optimization is a potential global optimization technique that has been widely used to address problems in a variety of fields. The idea of this research is to use exponential basis functions and the particle swarm optimization technique to find a numerical solution for the Sine-Gordan equation, whose numerical solutions show the soliton form and has diverse applications. The implemented optimization technique is employed to determine the involved parameter in the basis functions, which was previously approximated as a random number in the work reported till now in the literature. The obtained results are comparable with the results obtained in the literature. The work is presented in the form of figures and tables and is found encouraging.

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Keywords

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