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A modified variational iteration method for nonlinear oscillators
Chen Yanmao,Liu Jike * #
Department of Mechanics, Sun Yat-sen University, Guangzhou 510275, China
*Correspondence author
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Funding: none
Opened online: 5 January 2009
Accepted by: none
Citation: Chen Yanmao,Liu Jike.A modified variational iteration method for nonlinear oscillators[OL]. [ 5 January 2009] http://en.paper.edu.cn/en_releasepaper/content/27331
 
 
A modified variational iteration method (VIM) is proposed for nonlinear oscillators. Different from the existing VIM, the algebraic equation deduced at each iteration stage is always linear when the proposed procedure is applied to conservative oscillators. Taking the Duffing and the van der Pol equations as illustrative examples, very excellent approximations can be easily. In addition, it is proved the modified VIM is equivalent to a modified Mickens iteration. Furthermore, the modified VIM is extended by introducing an auxiliary parameter exemplified by two special examples. This parameter provides us with a convenient way to control the convergence of approximation series and adjust convergence rate when necessary. Consequently, the extended method is valid for both weakly and strongly nonlinear oscillators with either small or large amplitude.
Keywords:Variational iteration method; Mickens iteration procedure; Duffing equation; van der Pol equation
 
 
 

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