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Open AccessArticle

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