Construction of periodic solutions with a given accuracy by the method of the small parameter (Q1571155)

The author considers the problem of finding the range of values of the parameter \(\mu\) for nonlinear differential systems containing this small parameter \(\mu\) such that the norm of the difference between the exact and approximate periodic solutions does not exceed an a priori specified \(\delta\). In order to solve this problem, theorems on localization of exact solutions are proved. On the basis of these theorems, constructive algorithms for calculating periodic solutions with a given accuracy are constructed.