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

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...

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Bibliographic Details
Main Author: H. M. Abdelhafez
Format: Article
Language:English
Published: MDPI AG 2016-03-01
Series:Mathematics
Subjects:
Online Access:http://www.mdpi.com/2227-7390/4/1/11
Description
Summary: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.
ISSN:2227-7390