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.
Seher Durmaz. Metin Orhan Kaya. "High-Order Energy Balance Method to Nonlinear Oscillators." J. Appl. Math. 2012 (SI02) 1 - 7, 2012. https://doi.org/10.1155/2012/518684