Interval Wavelet Numerical Method on Fokker-Planck Equations for Nonlinear Random System | Zendy

Liwei Liu | Zendy

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Interval Wavelet Numerical Method on Fokker-Planck Equations for Nonlinear Random System

Author(s) -

Liwei Liu

Publication year - 2013

Publication title -

advances in mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.283

H-Index - 23

eISSN - 1687-9139

pISSN - 1687-9120

DOI - 10.1155/2013/651357

Subject(s) - fokker–planck equation , wavelet , mathematics , nonlinear system , interval (graph theory) , probability density function , mathematical analysis , collocation (remote sensing) , boundary (topology) , statistical physics , physics , partial differential equation , computer science , quantum mechanics , statistics , artificial intelligence , combinatorics , machine learning

The Fokker-Planck-Kolmogorov (FPK) equation governs the probability density function (p.d.f.) of the dynamic response of a particular class of linear or nonlinear system to random excitation. An interval wavelet numerical method (IWNM) for nonlinear random systems is proposed using interval Shannon-Gabor wavelet interpolation operator. An FPK equation for nonlinear oscillators and a time fractional Fokker-Planck equation are taken as examples to illustrate its effectiveness and efficiency. Compared with the common wavelet collocation methods, IWNM can decrease the boundary effect greatly. Compared with the finite difference method for the time fractional Fokker-Planck equation, IWNM can improve the calculation precision evidently

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