Improvement of Harmonic Balance Using Jacobian Elliptic Functions


We propose a method for finding approximate analytic solutions to autonomous single degree-of-freedom nonlinear oscillator equations. It consists of the harmonic balance with linearization in which Jacobian elliptic functions are used instead of circular trigonometric functions. We show that a simple change of independent variable followed by a careful choice of the form of anharmonic solution enable to obtain highly accurate approximate solutions. In particular our examples show that the proposed method is as easy to use as existing harmonic balance based methods and yet provides substantially greater accuracy.

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Yamgoué, S. , Nana, B. and Lekeufack, O. (2015) Improvement of Harmonic Balance Using Jacobian Elliptic Functions. Journal of Applied Mathematics and Physics, 3, 680-690. doi: 10.4236/jamp.2015.36081.

Conflicts of Interest

The authors declare no conflicts of interest.


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