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Journal of Applied Mathematics
Volume 2012, Article ID 518684, 7 pages
Research Article

High-Order Energy Balance Method to Nonlinear Oscillators

Faculty of Aeronautics and Astronautics, Istanbul Technical University, Maslak, 34469 Istanbul, Turkey

Received 1 April 2012; Revised 25 June 2012; Accepted 9 July 2012

Academic Editor: Livija Cveticanin

Copyright © 2012 Seher Durmaz and Metin Orhan Kaya. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.