Numerical path integration method based on bubble grids for nonlinear dynamical systems

A new numerical path integration method based on bubble grids for nonlinear dynamical systems is presented in this paper. The ordinary differential equations for the first and second order moments are derived on the basis of the Gaussian closure method. Then the probability density values on the bub...

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Bibliographic Details
Published inApplied mathematical modelling Vol. 37; no. 3; pp. 1490 - 1501
Main Authors Cai, Li, Nie, Yufeng, Xie, Wenxian, Zhang, Weiwei
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.02.2013
Subjects
Bubble grids
Bubbles
Density
Dynamical systems
Excitation
Harmonics
Mathematical models
Nonlinear dynamical systems
Nonlinearity
Path integration method
Stochasticity
Path integration method
Bubble grids
Nonlinear dynamical systems
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ISSN0307-904X
DOI10.1016/j.apm.2012.04.014

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Summary:A new numerical path integration method based on bubble grids for nonlinear dynamical systems is presented in this paper. The ordinary differential equations for the first and second order moments are derived on the basis of the Gaussian closure method. Then the probability density values on the bubble nodes in the computational domain can be calculated via the obtained method. The good performance of the resulting method is finally shown in the numerical examples by using some specific nonlinear dynamical systems: Duffing oscillator subjected to harmonic and stochastic excitations, and Duffing–Rayleigh oscillator subjected to harmonic and stochastic excitations.
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ISSN:0307-904X
DOI:10.1016/j.apm.2012.04.014