A modification of He's variational approach using the least square method to nonlinear oscillators

被引：5

作者：

Arif, Muhammad Shoaib ^{[1
]}

Nawaz, Yasir ^{[1
]}

Bibi, Mairaj ^{[2
]}

Fayyaz, Rabia ^{[2
]}

Naz, Mehvish ^{[2
]}

机构：

[1] Air Univ, Dept Math, PAF Complex E-9, Islamabad 44000, Pakistan

[2] Comsats Univ, Dept Math, Islamabad, Pakistan

来源：

JOURNAL OF LOW FREQUENCY NOISE VIBRATION AND ACTIVE CONTROL | 2019年 / 38卷 / 3-4期

关键词：

Variational method; global error minimization; nonlinear differential equations; nonlinear oscillators; HOMOTOPY-PERTURBATION METHOD; ITERATION METHOD; ENERGY-BALANCE; PRINCIPLES;

D O I：

10.1177/1461348419828222

中图分类号：

O42 [声学];

学科分类号：

070206 ; 082403 ;

摘要：

In this paper, we apply the global error minimization method to nonlinear oscillators with fractional terms for determining the first- and second-order approximate frequencies and solutions. The estimation problem is transformed into a minimization problem which leads to a simple yet precise scheme for finding the frequency of oscillation and the solution of the ordinary differential equation.

引用

页码：996 / 1007

页数：12

共 38 条

[1]

[Anonymous], 2012, ABSTR APPL ANAL

[2]

[Anonymous], INT J COMPUT MATH

[3] Application of a modified He's homotopy perturbation method to obtain higher-order approximations of an x1/3 force nonlinear oscillator [J].

Belendez, A. ;

Pascual, C. ;

Gallego, S. ;

Ortuno, M. ;

Neipp, C. .

PHYSICS LETTERS A, 2007, 371 (5-6) :421-426

[4] Application of He's homotopy perturbation method to the Duffing-harmonic oscillator [J].

Belendez, A. ;

Hernandez, A. ;

Belendez, T. ;

Fernandez, E. ;

Alvarez, M. L. ;

Neipp, C. .

INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, 2007, 8 (01) :79-88

[5] Harmonic balance approach to the periodic solutions of the (an)harmonic relativistic oscillator [J].

Belendez, Augusto ;

Pascual, Carolina .

PHYSICS LETTERS A, 2007, 371 (04) :291-299

[6] Determination of limit cycles for a modified van der Pol oscillator [J].

D'Acunto, M .

MECHANICS RESEARCH COMMUNICATIONS, 2006, 33 (01) :93-98

[7] Solution of the damped cubic-quintic Duffing oscillator by using Jacobi elliptic functions [J].

Elias-Zuniga, Alex .

APPLIED MATHEMATICS AND COMPUTATION, 2014, 246 :474-481

[8] Exact solution of the cubic-quintic Duffing oscillator [J].

Elias-Zuniga, Alex .

APPLIED MATHEMATICAL MODELLING, 2013, 37 (04) :2574-2579

[9] Global Error Minimization method for solving strongly nonlinear oscillator differential equations [J].

Farzaneh, Yadollah ;

Tootoonchi, Ali Akbarzadeh .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 59 (08) :2887-2895

[10]

Ganji DD, 2006, INT J NONLIN SCI NUM, V7, P411

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