A fast Galerkin method to obtain the periodic solutions of a nonlinear oscillator

摘要

This paper focuses on the determination of periodic solutions of nonlinear oscillators as well as on the qualitative analysis of their stability.These oscillators are modelled by the following differential equation (t) + k(t) + ∑j=13 ajj = g(t) being g(t) a T-periodic driving force.We develop an algorithm, based on the Galerkin method, using the Fast Fourier Transform (FFT), to calculate the periodic solutions of previous equation. Furthermore, we include a combined algorithm with fast convergence to solve the nonlinear algebraic equations obtained in the Fast Galerkin Algorithm.Finally, we validate this methodology using the algorithm to obtain the periodic solutions of a Duffing oscillator with chaotic behavior.