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

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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Main Author: H. M. Abdelhafez
Format: Article
Language:English
Published: MDPI AG 2016-03-01
Series:Mathematics
Subjects:
forced duffing oscillator
forced van der Pol Oscillator
Padé approximant
laplace transform
semi-analytical solution
Online Access:http://www.mdpi.com/2227-7390/4/1/11
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spelling doaj-0483c7d3270243c4b90a7bb9afc674ff2020-11-25T01:59:07ZengMDPI AGMathematics2227-73902016-03-01411110.3390/math4010011math4010011Solution of Excited Non-Linear Oscillators under Damping Effects Using the Modified Differential Transform MethodH. M. Abdelhafez0Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf 32952, EgyptThe 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.http://www.mdpi.com/2227-7390/4/1/11forced duffing oscillatorforced van der Pol OscillatorPadé approximantlaplace transformsemi-analytical solution
collection DOAJ
language English
format Article
sources DOAJ
author H. M. Abdelhafez
spellingShingle H. M. Abdelhafez
Solution of Excited Non-Linear Oscillators under Damping Effects Using the Modified Differential Transform Method
Mathematics
forced duffing oscillator
forced van der Pol Oscillator
Padé approximant
laplace transform
semi-analytical solution
author_facet H. M. Abdelhafez
author_sort H. M. Abdelhafez
title Solution of Excited Non-Linear Oscillators under Damping Effects Using the Modified Differential Transform Method
title_short Solution of Excited Non-Linear Oscillators under Damping Effects Using the Modified Differential Transform Method
title_full Solution of Excited Non-Linear Oscillators under Damping Effects Using the Modified Differential Transform Method
title_fullStr Solution of Excited Non-Linear Oscillators under Damping Effects Using the Modified Differential Transform Method
title_full_unstemmed Solution of Excited Non-Linear Oscillators under Damping Effects Using the Modified Differential Transform Method
title_sort solution of excited non-linear oscillators under damping effects using the modified differential transform method
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2016-03-01
description 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.
topic forced duffing oscillator
forced van der Pol Oscillator
Padé approximant
laplace transform
semi-analytical solution
url http://www.mdpi.com/2227-7390/4/1/11
work_keys_str_mv AT hmabdelhafez solutionofexcitednonlinearoscillatorsunderdampingeffectsusingthemodifieddifferentialtransformmethod
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