Homotopy perturbation method for strongly nonlinear oscillators

被引：74

作者：

He, Ji-Huan ^{[1
,2
,3
]}

Jiao, Man-Li ^{[1
]}

Gepreel, Khaled A. ^{[4
]}

Khan, Yasir ^{[5
]}

机构：

[1] Xian Univ Architecture & Technol, Sch Sci, Xian, Peoples R China

[2] Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo, Peoples R China

[3] Soochow Univ, Coll Text & Clothing Engn, Natl Engn Lab Modern Silk, 199 Ren Ai Rd, Suzhou, Peoples R China

[4] Taif Univ, Coll Sci, Dept Math, POB 11099, Taif 21944, Saudi Arabia

[5] Univ Hafr Al Batin, Dept Math, Hafar al Batin 31991, Saudi Arabia

来源：

MATHEMATICS AND COMPUTERS IN SIMULATION | 2023年 / 204卷

关键词：

Cubic-quintic nonlinear oscillators; Homotopy perturbation method; Periodic solution; VARIATIONAL ITERATION METHOD; HE-LAPLACE METHOD; DUFFING OSCILLATOR; VIBRATION;

D O I：

10.1016/j.matcom.2022.08.005

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

This paper reveals the effectiveness of the homotopy perturbation method for strongly nonlinear oscillators. A generalized Duffing oscillator is adopted to elucidate the solving process step by step, and a nonlinear frequency-amplitude relationship is obtained with a relative error of 0.91% when the amplitude tends to infinity, the solution morphology is also discussed, and the zero-th approximate solution is enough for conservative nonlinear oscillators, while the accuracy of the frequency can be improved if the iteration continues. (c) 2022 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

引用

页码：243 / 258

页数：16

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