Homotopy Analysis Method for a Conservative Nonlinear Oscillator with Fractional Power
Open Access
- 1 January 2021
- journal article
- research article
- Published by Scientific Research Publishing, Inc. in Journal of Applied Mathematics and Physics
- Vol. 09 (01), 31-40
- https://doi.org/10.4236/jamp.2021.91004
Abstract
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 u1/3. 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.Keywords
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