A GOOD INITIAL GUESS FOR APPROXIMATING NONLINEAR OSCILLATORS BY THE HOMOTOPY PERTURBATION METHOD

被引：35
|
作者：
He, Ji-Huan [1 ,2 ,3 ]
He, Chun-Hui [1 ,4 ,5 ]
Alsolami, Abdulrahman Ali [5 ]
机构：
[1] Soochow Univ, Coll Text & Clothing Engn, Natl Engn Lab Modern Silk, Suzhou, Peoples R China
[2] Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo, Peoples R China
[3] Xian Univ Architecture & Technol, Sch Sci, Xian, Peoples R China
[4] China Univ Min & Technol, Sch Math, Xuzhou, Jiangsu, Peoples R China
[5] King Abdulaziz Univ, Fac Sci, Dept Math, Jeddah, Saudi Arabia
来源：
FACTA UNIVERSITATIS-SERIES MECHANICAL ENGINEERING | 2023年 / 21卷 / 01期
关键词：
Homotopy perturbation method; Nonlinear oscillator; Periodic solution; VARIATIONAL ITERATION METHOD; EQUATIONS;
D O I：
10.22190/FUME230108006H
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
A good initial guess and an appropriate homotopy equation are two main factors in applications of the homotopy perturbation method. For a nonlinear oscillator, a cosine function is used in an initial guess. This article recommends a general approach to construction of the initial guess and the homotopy equation. Duffing oscillator is adopted as an example to elucidate the effectiveness of the method.
引用
收藏
页码：21 / 29
页数：9
相关论文
共 50 条
  • [31] An Optimal Choice of Initial Solutions in the Homotopy Perturbation Method
    Hesameddini, Esmail
    Latifizadeh, Habibolla
    INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, 2009, 10 (11-12) : 1389 - 1398
  • [32] A heuristic review on the homotopy perturbation method for non-conservative oscillators
    He, Chun-Hui
    El-Dib, Yusry O.
    JOURNAL OF LOW FREQUENCY NOISE VIBRATION AND ACTIVE CONTROL, 2022, 41 (02) : 572 - 603
  • [33] Multistage homotopy perturbation method for nonlinear reaction networks
    Lee, Chang Hyeong
    Park, Kyung Duk
    Jang, Bongsoo
    JOURNAL OF MATHEMATICAL CHEMISTRY, 2013, 51 (07) : 1945 - 1960
  • [34] Application of modified homotopy perturbation method to nonlinear oscillations
    Marinca, V
    ARCHIVES OF MECHANICS, 2006, 58 (03): : 241 - 256
  • [35] OPTIMAL HOMOTOPY PERTURBATION METHOD FOR NONLINEAR PROBLEMS WITH APPLICATIONS
    Marinca, Vasile
    Ene, Remus-Daniel
    Marinca, Bogdan
    APPLIED AND COMPUTATIONAL MATHEMATICS, 2022, 21 (02) : 123 - 136
  • [36] Homotopy perturbation method: a new nonlinear analytical technique
    He, JH
    APPLIED MATHEMATICS AND COMPUTATION, 2003, 135 (01) : 73 - 79
  • [37] Application of homotopy perturbation method to nonlinear wave equations
    He, JH
    CHAOS SOLITONS & FRACTALS, 2005, 26 (03) : 695 - 700
  • [38] Multistage homotopy perturbation method for nonlinear reaction networks
    Chang Hyeong Lee
    Kyung Duk Park
    Bongsoo Jang
    Journal of Mathematical Chemistry, 2013, 51 : 1945 - 1960
  • [39] HOMOTOPY PERTURBATION METHOD FOR SOLVING A NONLINEAR SYSTEM FOR AN EPIDEMIC
    Alshomrani, Nada A. M.
    Alharbi, Weam G.
    Alanazi, Ibtisam M. A.
    Alyasi, Lujain S. M.
    Alrefaei, Ghadi N. M.
    Alamri, Seada A.
    Alanzi, Asmaa H. Q.
    ADVANCES IN DIFFERENTIAL EQUATIONS AND CONTROL PROCESSES, 2024, 31 (03): : 347 - 355
  • [40] The Homotopy Perturbation Method for Solving Singular Initial Value Problems
    Yildirim, Ahmet
    Agirseven, Deniz
    INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, 2009, 10 (02) : 235 - 238
12345