Author(s)

Huaxiong Chen, Yanyan Wang

School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, China.

In this paper, the homotopy analysis method is applied to deduce the periodic solutions of a conservative nonlinear oscillator for which the elastic force term is proportional to u^1/3. By introducing the auxiliary linear operator and the initial guess of solution, the homotopy analysis solving is set up. By choosing the suitable convergence-control parameter, the accurate high-order approximations of solution and frequency for the whole range of initial amplitudes can easily be obtained. Comparison of the results obtained using this method with those obtained by different methods reveals that the former is more accurate, effective and convenient for these types of nonlinear oscillators.

Homotopy Analysis Method, Approximate Solutions, Fractional Power, Nonlinear Oscillation

Chen, H. and Wang, Y. (2021) Homotopy Analysis Method for a Conservative Nonlinear Oscillator with Fractional Power. Journal of Applied Mathematics and Physics, 9, 31-40. doi: 10.4236/jamp.2021.91004.