Evidence map›Paper›PMID 38228710›Full record

ArticleScientific reports2024

Critical analysis for nonlinear oscillations by least square HPM.

Muhammad Rafiq, Muhammad Kamran, Hijaz Ahmad, Afis Saliu

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Article in Scientific reports, 2024. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.

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1 · What the graph read from it

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4 · The record

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5 · Who and what money

Authors and funding

4 authors.

Muhammad RafiqDepartment of Mathematics, COMSATS University Islamabad, Wah Campus, Islamabad, Pakistan.
Muhammad KamranDepartment of Mathematics, COMSATS University Islamabad, Wah Campus, Islamabad, Pakistan.
Hijaz AhmadDepartment of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, Saudi Arabia.
Afis SaliuDepartment of Mathematics, University of the Gambia, MDI Road, P.O. Box 3530, Kanifing, Serrekunda, The Gambia. asaliu@utg.edu.gm.

Funding

No grant is acknowledged in the PubMed record.

6 · The paper itself

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.

Identifiers

PMID38228710
PMCPMC10791672

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