Nonlinear oscillation via Volterra series

Using a novel approach, the amplitude and frequency of nearly sinusoidal nonlinear oscillators can be calculated by solving two algebraic nonlinear equations. These determining equations can be generated to within any desired accuracy using a recursive algorithm based on Volterra series. Our method inherits many desirable features of the harmonic balance method, the describing function method, and the averaging method. Our technique is analogous to, but is much simpler than, the classic approach due to Krylov, Bogoliubov, and Mitropolsky. Unlike conventional techniques, however, our approach imposes no severe restriction on either the degree of nonlinearity, or the amplitude of oscillation. Moreover, the accuracy of the solution can be determined by a constructive algorithm.