FPK方程的近似闭合解

Approximation Solution of FPK Equations

讨论了FPK方程的近似闭合解问题。假设FPK方程的解具有指数多项式的形式 ,利用比较系数的方法确定其中待定的常数。计算表明 ,本方法适用于强非线性系统 ,在特殊情形下还能求出原方程的精确解。

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.