The barycentric interpolation collocation method for a class of nonlinear vibration systems

A nonlinear vibration system arises in physics. Besides its mathematical model, it is of great importance to have an accurate and reliable solution to the system. Though there are many analytical methods, such as the variational iteration method and the homotopy perturbation method, numerical approa...

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Bibliographic Details
Published inJournal of low frequency noise, vibration, and active control Vol. 38; no. 3-4; pp. 1495 - 1504
Main Authors Wu, Hongchun, Wang, Yulan, Zhang, Wei, Wen, Tao
Format Journal Article
LanguageEnglish
Published London, England SAGE Publications 01.12.2019
Sage Publications Ltd
SAGE Publishing
Subjects
Collocation methods
Duffing equation
Interpolation
Iterative methods
Nonlinear systems
Oscillators
Perturbation methods
Vibration
numerical solution
direct linearized iterative
vibration system
barycentric interpolation collocation method
Duffing equation
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Summary:A nonlinear vibration system arises in physics. Besides its mathematical model, it is of great importance to have an accurate and reliable solution to the system. Though there are many analytical methods, such as the variational iteration method and the homotopy perturbation method, numerical approaches are rare. This paper suggests the barycentric interpolation collocation method to solve nonlinear oscillators. The Duffing equation is adopted as an example to elucidate the solution process. Some numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by the method indicate the method is simple and effective.
ISSN:1461-3484
2048-4046
DOI:10.1177/1461348418824898