文献类型：期刊文献

英文题名：A Modified Variational Iteration Method for Nonlinear Oscillators

作者：Yang, Q. W.[1];Chen, Y. M.[2];Liu, J. K.[2];Zhao, W.[3]

机构：[1]Shaoxing Univ, Dept Civil Engn, Shaoxing 312000, Peoples R China;[2]Sun Yat Sen Univ, Dept Mech, Guangzhou, Guangdong, Peoples R China;[3]Jinan Univ, Key Lab Disaster Forecast & Control Engn, Minist Educ China, Guangzhou, Guangdong, Peoples R China

年份：2013

卷号：14

期号：7-8

起止页码：453

外文期刊名：INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION

收录：SCI-EXPANDED(收录号：WOS:000328632100003)、、Scopus(收录号：2-s2.0-84892662660)、WOS

基金：This work is supported by the National Natural Science Foundation of China (11002088, 10102023, 10972241, 11032005), Zhejiang Province Natural Science Foundation (Y1110949), the scientific research project of Shaoxing City (2010A23006), Foundation for Distinguished Young Talents in Higher Education of Guangdong, China (34310018), Doctoral Program Foundation of Ministry of Education of China (20090171110042).

语种：英文

外文关键词：variational iteration method; Mickens iteration procedure; Duffing equation; van der Pol equation

外文摘要：A modified variational iteration method (MVIM) is proposed for nonlinear oscillators. Different from the existing VIM, the algebraic equation deduced at each iteration stage is always linear when the proposed approach is applied to conservative oscillators. Therefore, highly accurate approximations can be easily obtained. The Duffing and the van der Pol equations are presented to validate the MVIM. Numerical examples show that the presented method is valid for both weakly and strongly nonlinear oscillators. In addition, it reveals that the MVIM is equivalent to a modified Mickens iteration scheme. Furthermore, the MVIM is extended by means of an auxiliary parameter. This parameter provides us with a convenient way to control and adjust the convergence of VIM approximations when necessary.