High-order energy balance method to nonlinear oscillators

Energy balance method (EBM) is extended for high-order nonlinear oscillators. To illustrate the effectiveness of the method, a cubic-quintic Duffing oscillator was chosen. The maximum relative errors of the frequencies of the oscillator read 1.25 and 0.6 for the first- and second-order approximation, respectively. The third-order approximation has an accuracy as high as 0.008. Excellent agreement of the approximated frequencies and periodic solutions with the exact ones is demonstrated for several values of parameters of the oscillator.