Application of He's Variational Iteration Method for Solving Nonlinear BBMB Equations and Free Vibration of Systems

被引：14
作者：
Ganji, D. D. [1 ]
Babazadeh, H. [1 ]
Jalaei, M. H. [1 ]
Tashakkorian, H. [1 ]
机构：
[1] Babol Univ Technol, Fac Mech & Elect Engn, Babol Sar, Iran
来源：
ACTA APPLICANDAE MATHEMATICAE | 2009年 / 106卷 / 03期
关键词：
He's variational iteration method; Benjamin-Bona-Mahony-Burgers (BBMB) equations; Serial linear and nonlinear stiffness; Nonlinear free vibration; Motion equation; HOMOTOPY PERTURBATION METHOD; TRAVELING-WAVE SOLUTIONS; EXPLICIT;
D O I：
10.1007/s10440-008-9303-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A new analytical method called He's variational iteration method (VIM) is introduced to be applied to solve nonlinear Benjamin-Bona-Mahony-Burgers (BBMB) equations and free vibration of a nonlinear system having combined linear and nonlinear springs in series in this article. In this method, general Lagrange multipliers are introduced to construct correction functionals for the problems. The multipliers can be identified optimally via the variational theory. The results are compared with the results of the homotopy analysis method and also with the exact solution. He's Variational iteration method in this problem functions so better than the homotopy analysis method and exact solutions one of them in per section.
引用
收藏
页码：359 / 367
页数：9
相关论文
共 24 条
[1]   A REVIEW OF THE DECOMPOSITION METHOD IN APPLIED-MATHEMATICS [J].
ADOMIAN, G .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1988, 135 (02) :501-544
[2]  
Adomian G., 1994, Solving Frontier Problems of Physics: the Decomposition Method
[3]   Exact and numerical traveling wave solutions of Whitham-Broer-Kaup equations [J].
El-Sayed, SM ;
Kaya, D .
APPLIED MATHEMATICS AND COMPUTATION, 2005, 167 (02) :1339-1349
[4]   Approximate explicit solutions of nonlinear BBMB equations by homotopy analysis method and comparison with the exact solution [J].
Fakhari, A. ;
Domairry, Ganji ;
Ebrahimpour .
PHYSICS LETTERS A, 2007, 368 (1-2) :64-68
[5]  
GANJI DD, 2006, J COMPUT APPL MATH
[6]  
Ghasemi, 2008, INT J NONLINEAR DYN, V1, P79
[7]  
Hagedorn P., 1988, NONLINEAR OSCILLATIO
[8]   Variational iteration method for autonomous ordinary differential systems [J].
He, JH .
APPLIED MATHEMATICS AND COMPUTATION, 2000, 114 (2-3) :115-123
[9]   Variational iteration method - a kind of non-linear analytical technique: Some examples [J].
He, JH .
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 1999, 34 (04) :699-708
[10]   Homotopy perturbation method for solving boundary value problems [J].
He, JH .
PHYSICS LETTERS A, 2006, 350 (1-2) :87-88
123