Abstract
Recently, the max-min approach was systematically studied in the review article (Ji-Huan, 2012). This paper concludes that He's max-min approach is also a very much effective method for nonlinear oscillators with discontinuous terms.
The ancient Chinese mathematics revives modern applications [1–8]; hereby, we show that He’s max-min approach [1, 9–11] is also very effective for nonlinear oscillators with discontinuous terms.
The max-min approach was first proposed in 2008 based on an ancient Chinese mathematics, and it has become a well-known method for nonlinear oscillators; see, for example, [12–14].
To illustrate the basic idea of the max-min approach [1], we consider the following nonlinear oscillator: By a similar treatment as given in [1], we have where is the unknown frequency.
According to an ancient Chinese inequality [1, 8, 10, 11], we have where , and are constants.
According to He’s max-min approach, we set or from which the frequency can be determined approximately as which is the same as that obtained by the homotopy perturbation method [15].