Open Access   Article

Applications of the Aboodh Transform and the Homotopy Perturbation Method to the Nonlinear Oscillators

P.K. Bera1 , S.K. Das2 , P. Bera3

1 Dept. of Physics, Dumkal College, Murshidabad, India.
2 Dept. of Mechanical Engineering, IIT Ropar, Rupnagar, India.
3 School of Electronics Engineering, VIT University, Vellore, India.

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Section:Research Paper, Product Type: Journal Paper
Volume-6 , Issue-1 , Page no. 1-10, Jan-2018


Online published on Jan 31, 2018

Copyright © P.K. Bera, S.K. Das, P. Bera . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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IEEE Style Citation: P.K. Bera, S.K. Das, P. Bera, “Applications of the Aboodh Transform and the Homotopy Perturbation Method to the Nonlinear Oscillators”, International Journal of Computer Sciences and Engineering, Vol.6, Issue.1, pp.1-10, 2018.

MLA Style Citation: P.K. Bera, S.K. Das, P. Bera "Applications of the Aboodh Transform and the Homotopy Perturbation Method to the Nonlinear Oscillators." International Journal of Computer Sciences and Engineering 6.1 (2018): 1-10.

APA Style Citation: P.K. Bera, S.K. Das, P. Bera, (2018). Applications of the Aboodh Transform and the Homotopy Perturbation Method to the Nonlinear Oscillators. International Journal of Computer Sciences and Engineering, 6(1), 1-10.

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In this paper, the differential equation of motion of the classical Helmholtz-Duffing oscillator, Van der Pol, Duffing oscillator and Duffing-Van der Pol oscillator equations have been solved analytically with the help of a new integral transform named Aboodh transform and homotopy perturbation method. By recasting the governing equations as nonlinear eigenvalue problems, we have obtained the excellent approximate analytical solution of the displacement and the relation between amplitude and angular frequency. We have also compared our results with exact numerical results graphically for few cases. Here, we have also demonstrated the sophistication and simplicity of this technique.

Key-Words / Index Term

Aboodh Transform, Homotopy Perturbation Method, Helmholtz-Duffing Oscillator, Van der Pol, Duffing Oscillator, Duffing-Van der Pol Oscillator, Approximate Analytical Solution


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