An alternative approach to averaging in nonlinear systems using classical probability density (Q6577044)

A new approach for the computation of the averaging integral involved in the application of the averaging method is proposed in this paper. It relies on the classical probability density of the ``fast'' variable. The equivalence between the averaging integral and the cross-correlation product of the classical probability density and the target function is proved. This equivalence simplifies handling many problems, particularly those involving piecewise-defined target functions. An effective numerical method to calculate the averaged function is also proposed.