A modified methof of averaging for solving a class of nonlinear equations (Q1804445)

The author presents a new modified averaging method generalizing the well-known Bogolyubov-Krylov and Bogolyubov-Krylov-Mitropolskij methods for a class of equations \(d^ 2 u/dt^ 2+ \omega^ 2 u= \varepsilon f(u, du/dt, d^ 2 u/dt^ 2)\), where \(\varepsilon\) is a small parameter, \(f(x, y, z)\) is an analytical function of three arguments. Two examples are given to demonstrate the uniform convergence of the expansions and a comparison of the proposed methods with the method of multiple scales.