Once again on the Samoilenko numerical-analytic method of successive periodic approximations - Korol', I. I.; Perestyuk, N. A. (Ukrains’kyi Matematychnyi Zhurnal, 2006)
A new numerical-analytic algorithm for the investigation of periodic solutions of nonlinear periodic systems of differential equations dx/dt = A(t) x+ ƒ(t, x) in the critical case is developed. The problem of the existence of solutions and their approximate construction is studied. Estimates for the convergence of successive periodic approximations are obtained.