Krylov–Bogolyubov averaging

Summary

Krylov–Bogolyubov averaging is a method for differential equations with a small parameter and a fast periodic dependence on time. It replaces the right-hand side by its average over one period and studies the simpler averaged equation. The averaging theorem says that solutions of the two equations stay close over long time intervals, of length of order $1/\varepsilon$. It is a basic tool for weakly nonlinear oscillations in mechanics and physics. See the definition.