The method of successive approximations for the asymptotic integration of quasilinear autonomous systems

Abstract

THE algorithm for the application of the Krylov-Bogolyubov method [1, 2] for investigating multifrequency oscillatory processes is considered for systems with a non-analytic non-linearity characteristic, where, instead of finding the unknown solutions as series of powers of a small parameter, it is proposed to use the method of successive approximations. The asymptotic nature of the approximate solutions obtained by this method is demonstrated.