Analytical approximate approach to the Helmholtz-Duffing oscillator. (English) Zbl 07907677
Singh, Jagdev (ed.) et al., Advances in mathematical modelling, applied analysis and computation. Proceedings of the fourth conference, ICMMAAC 2021, JECRC University, Jaipur, India, August 5–7, 2021. Singapore: Springer. Lect. Notes Netw. Syst. 415, 395-412 (2023).
Summary: In this paper, a novel analytical approximation for the period and periodic solutions for the Helmholtz-Duffing oscillator is presented. The main idea of present work is to approximate the integration in exact analytical period of equation using a well-known quadrature rules. This approach gives us not only the accurate period of motion but also a truly periodic solution in a rational form as a function of the amplitude of oscillation. Comparison of the result obtained using this approach with the exact one and existing results reveals that the high accurate, simplicity, and efficiency of the proposed procedure for the whole range of initial amplitudes and the equation parameter in a variety of cases. The method can be easily extended to other strongly nonlinear oscillators.
For the entire collection see [Zbl 1522.00198].
For the entire collection see [Zbl 1522.00198].
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 34A34 | Nonlinear ordinary differential equations and systems |
| 65D30 | Numerical integration |
Keywords:
highly nonlinear oscillators; analytical approximate solutions; periodic solution; numerical integration; Helmholtz-Duffing oscillatorReferences:
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