Error bounds of the finite-difference method in the problem of approximate construction of forced oscillations in nonlinear systems

The study considers the finite-difference method in the problem of approximate construction of forced oscillation modes in nonlinear systems described by differential equations of the form with a constant matrix A and a nonlinearity f T-periodic in t. A guaranteed bound on the error of the method is derived for the case of a weak nonlinearity f.The study was financially supported by the Russian Foundation of Basic Research (93-012-869).Translated from Nelineinye Dinamicheskie Sistemy: Kachestvennyi Analiz i Upravlenie — Sbornik Trudov, No. 2, pp. 81–85, 1993.