Critical analysis for nonlinear oscillations by least square HPM

Muhammad Rafiq; Muhammad Kamran; Hijaz Ahmad; Afis Saliu

doi:10.1038/s41598-024-51706-3

Critical analysis for nonlinear oscillations by least square HPM

Sci Rep. 2024 Jan 17;14(1):1456. doi: 10.1038/s41598-024-51706-3.

Authors

Muhammad Rafiq¹, Muhammad Kamran¹, Hijaz Ahmad^{2

3

4

5}, Afis Saliu⁶

Affiliations

¹ Department of Mathematics, COMSATS University Islamabad, Wah Campus, Islamabad, Pakistan.
² Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, Saudi Arabia.
³ Near East University, Operational Research Center in Healthcare, TRNC Mersin 10, Nicosia, 99138, Turkey.
⁴ Center for Applied Mathematics and Bioinformatics, Gulf University for Science and Technology, Mishref,, Kuwait.
⁵ Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon.
⁶ Department of Mathematics, University of the Gambia, MDI Road, P.O. Box 3530, Kanifing, Serrekunda, The Gambia. asaliu@utg.edu.gm.

Abstract

In this study, a novel adapted homotopy perturbation method (HPM) is used to treat the nonlinear phenomena of free vibration in a system with one degree of freedom. This adaptation involves the integration of HPM with a least-squares optimizer, resulting in a hybrid method called the least square homotopy perturbation method (LSHPM). The LSHPM is tested on various nonlinear problems documented in the existing literature. To evaluate the effectiveness of the proposed approach, the identified problems are also tackled using HPM and the MATLAB built-in function bvp5c, and then the results are compared with those obtained using LSHPM. In addition, a comparative analysis is carried out with the results of the AG method as found in the literature. The results show that LSHPM is a reliable and efficient method suitable for solving more complicated initial value problems in the fields of science and engineering.