Lai, S.K., Lim, C.W., Wu, B.S., Wang, C., Zeng, Q.C. and He, X.F. (2009) Newton-Harmonic Balancing Approach for Accurate Solutions to Nonlinear Cubic-Quintic Doffing Oscillators. Applied Mathematical Modelling, 33, 852-866. http://dx.doi.org/10.1016/j.apm.2007.12.012

has been cited by the following article:

• TITLE: Improvement of Harmonic Balance Using Jacobian Elliptic Functions

  AUTHORS: Serge Bruno Yamgoué, Bonaventure Nana, Olivier Tiokeng Lekeufack

  KEYWORDS: Harmonic Balance, Linearization, Continuous Force Function, Single Degree-of-Freedom, Conservative System, Jacobian Elliptic Functions, Symmetric Oscillations

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.3 No.6, June 26, 2015

  ABSTRACT: 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.