The probability density function (PDF) of the response of non-linear stochastic oscillator excited by white noise is assumed to be an exponential function of polynomials. Weight functions are used to make the FPK equation satisfied in the weak sense of integration with the assumed PDF. Example is given to show the application of the method to non-linear oscillator. The PDFs obtained with the proposed method and conventional Caussian closure method are compared with exact one in special case. Numerical results showed that the PDF obtained with the proposed method are much close to the exact PDF. In some cases, even exact results can be obtained with the proposed method.
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