Higher order averaging method of coefficients in Fokker-Planck equation

Two methods of integrating the first-order averaged Fokker-Planck (FP) equation used in the theory of random oscillations are proposed for the non-autonomous cases. Further, since the effect of some nonlinear terms is lost during the first-order averaging procedure, the procedures for obtaining higher approximate solutions to the FP equation are developed. It is shown that these procedures involve the classical first-order averaging method of coefficients in FP equation. The Duffing and Van der Pol oscillations are considered.