A Hybrid Approach for Solution of Fokker-Planck Equation

Abstract

Quantification of response statistics of non-linear systems subjected to harmonic, parametric and random excitation is of great importance in the field of stochastic dynamics. It is a well-known fact that probability density function of the stochastic response of non-linear systems subjected to white and coloured noise excitation is governed by both forward Fokker-Planck (FP) and backward Kolmogorov equations. This paper presents a novel approach, referred here as recursive decomposition method (RDM), for the solution of FP equation. The proposed approach decomposes the solution into number of component functions and determines the component functions in a recursive way. Unlike some of the traditional techniques, where the solutions are obtained at grid points, RDM yields the solution in a series form. Three examples illustrate the proposed approach for the solution of FP equation.