Mathematics

On explicit estimates of the approximation accuracy in first Bogolyubov's theorem

P. S. Krasil'nikov

Moscow Aviation Institute (National Research University)

Abstract: The problem of explicit estimates for the approximation accuracy in the averaging method of Bogolyubov standard systems is investigated. It is shown that estimates depends on some parameter $ \Lambda^* $, which affects the convergence of the time average. We formulate a statement on the explicit estimates for the approximation accuracy (Volosov's hypothesis). Hypothesis is proved under some additional restrictions on the right-hand side of differential equations.

Keywords: time average, the accuracy of the approximation, the averaging method.

UDC: 517.928.7

Received: 10.12.2015

Bibliographic databases:

•