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Mathematics 2016, 4(1), 11; doi:10.3390/math4010011

Solution of Excited Non-Linear Oscillators under Damping Effects Using the Modified Differential Transform Method

Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf 32952, Egypt
Academic Editor: Reza Abedi
Received: 14 December 2015 / Revised: 19 February 2016 / Accepted: 24 February 2016 / Published: 2 March 2016
(This article belongs to the Special Issue Applied Mathematics and Mechanics)
View Full-Text   |   Download PDF [1104 KB, uploaded 2 March 2016]   |  

Abstract

The modified differential transform method (MDTM), Laplace transform and Padé approximants are used to investigate a semi-analytic form of solutions of nonlinear oscillators in a large time domain. Forced Duffing and forced van der Pol oscillators under damping effect are studied to investigate semi-analytic forms of solutions. Moreover, solutions of the suggested nonlinear oscillators are obtained using the fourth-order Runge-Kutta numerical solution method. A comparison of the result by the numerical Runge-Kutta fourth-order accuracy method is compared with the result by the MDTM and plotted in a long time domain. View Full-Text
Keywords: forced duffing oscillator; forced van der Pol Oscillator; Padé approximant; laplace transform; semi-analytical solution forced duffing oscillator; forced van der Pol Oscillator; Padé approximant; laplace transform; semi-analytical solution
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. (CC BY 4.0).

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Abdelhafez, H.M. Solution of Excited Non-Linear Oscillators under Damping Effects Using the Modified Differential Transform Method. Mathematics 2016, 4, 11.

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