Homotopy perturbation method with three expansions

被引：85
作者：
He, Ji-Huan [1 ,2 ,3 ]
El-Dib, Yusry O. [4 ]
机构：
[1] Xian Univ Architecture & Technol, Sch Sci, Xian, Peoples R China
[2] Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo, Henan, Peoples R China
[3] Soochow Univ, Coll Text & Clothing Engn, Natl Engn Lab Modern Silk, 199 Ren Ai Rd, Suzhou, Peoples R China
[4] Ain Shams Univ, Fac Educ, Dept Math, Cairo, Egypt
来源：
JOURNAL OF MATHEMATICAL CHEMISTRY | 2021年 / 59卷 / 04期
关键词：
Homotopy Perturbations Method; Exponential Decay Parameter; Damping Duffing Equation; Frequency Expansion method; Amplitude Expansion Method;
D O I：
10.1007/s10910-021-01237-3
中图分类号：
O6 [化学];
学科分类号：
0703 ;
摘要：
A modification of the homotopy perturbation method is suggested with three effective expansions to solve a nonlinear oscillator with damping terms to expand the solution, the frequency and the amplitude. The Duffing equation with linear damping is used as an example to illustrate the simple solution process and effective results. The analysis exhibits that the amplitude behaves as an exponential decay with the damping parameter. This scheme yields a more effective result for the nonlinear oscillators and overcomes the shortcoming in some problems.
引用
收藏
页码：1139 / 1150
页数：12
相关论文
共 39 条
[1]   LI-HE'S MODIFIED HOMOTOPY PERTURBATION METHOD FOR DOUBLY-CLAMPED ELECTRICALLY ACTUATED MICROBEAMS-BASED MICROELECTROMECHANICAL SYSTEM [J].
Anjum, Naveed ;
He, Ji-Huan ;
Ain, Qura Tul ;
Tian, Dan .
FACTA UNIVERSITATIS-SERIES MECHANICAL ENGINEERING, 2021, 19 (04) :601-612
[2]   Laplace transform: Making the variational iteration method easier [J].
Anjum, Naveed ;
He, Ji-Huan .
APPLIED MATHEMATICS LETTERS, 2019, 92 :134-138
[3]  
[Anonymous], FRACTALS
[4]  
[Anonymous], 1918, ERZWUNGE SCHWEINGUNG
[5]  
El- Dib Y. O., 2017, NONLINEAR SCI LETT A, V8, p352
[6]  
El-Dib YO., 2018, NONLINEAR SCI LETT, V9, P219
[7]   EFFECT OF FRACTIONAL DERIVATIVE PROPERTIES ON THE PERIODIC SOLUTION OF THE NONLINEAR OSCILLATIONS [J].
El-Dib, Yusry O. ;
Elgazery, Nasser S. .
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2020, 28 (07)
[8]   Modified multiple scale technique for the stability of the fractional delayed nonlinear oscillator [J].
El-Dib, Yusry O. .
PRAMANA-JOURNAL OF PHYSICS, 2020, 94 (01)
[9]   Stability Configuration of a Rocking Rigid Rod over a Circular Surface Using the Homotopy Perturbation Method and Laplace Transform [J].
El-Dib, Yusry O. ;
Moatimid, Galal M. .
ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING, 2019, 44 (07) :6581-6591
[10]   Stability approach for periodic delay Mathieu equation by the He- multiple-scales method [J].
El-Dib, Yusry O. .
ALEXANDRIA ENGINEERING JOURNAL, 2018, 57 (04) :4009-4020
1234