Approximation Solution of FPK Equations
Rong Haiwu(1,2),Meng Guang(2),Wang Xiangdong(1),Xu Wei(3),Fang Tong(3)
(1,Department of Mathematics, Foshan University, Guangdong, 528000)
(2,The State Key Laboratory of Vibration, Shock and Noise, Shanghai Jiaotong University, Shanghai, 200030)
(3,Department of Mathematics, Northwestern Polytechnical University, Xi'an, 710072)

Abstract: The probability density function (PDF) of the responses of nonlinear system excited by white noise is approximated with the exponential function of polynomial in state variable. Instead of solving FPK equation directly, the approximate PDF is substituted into FPK equation and unknown parameters are factored out. Numerical results show that the PDFs obtained with the proposed method can be very close to the exact ones regardless of the degree of system non-linearity. In some cases, even exact solution can be obtained with the proposed method.
Keywords: FPK equation, probability density function, exponential function of polynomial.