https://doi.org/10.1140/epjp/i2019-12824-6
Regular Article
Study of strongly nonlinear oscillators using the Aboodh transform and the homotopy perturbation method
1
Department of Physics, Indian Institute of Information Technology Design and Manufacturing Kancheepuram, 600127, Chennai, Tamil Nadu, India
2
Department of Physics, Dumkal College, Basantapur, Dumkal, 742303, Murshidabad, West Bengal, India
3
School of Electronics Engineering, VIT University, 623014, Vellore, Tamil Nadu, India
4
Department of Mechanical Engineering, IIT Ropar, 140001, Rupnagar, Punjab, India
* e-mail: tapassil@iiitdm.ac.in
Received:
9
May
2019
Accepted:
13
June
2019
Published online:
25
September
2019
A generalized equation is constructed for a class of classical oscillators with strong anharmonicity which are not exactly solvable. The Aboodh transform-based homotopy perturbation method (ATHPM) is applied to get the approximate analytical solution for the generalized equation and hence some physically relevant anharmonic oscillators are studied as the special cases of this solution. ATHPM provides the approximate analytical solution of the generalized equation in a simple way. The solution from this simple method not only shows excellent agreement with the numerical results but is also found to be of better accuracy in comparison to the solutions obtained from other established approximation methods whenever compared for physically relevant special cases.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2019