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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 651357, 7 pages
http://dx.doi.org/10.1155/2013/651357
Research Article

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

Department of Mechanical Engineering, North China Institute of Aerospace Engineering, Langfang, Hebei 065000, China

Received 3 August 2013; Accepted 19 September 2013

Academic Editor: Carlo Cattani

Copyright © 2013 Li-wei Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.