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

H. M. Abdelhafez
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H. M. Abdelhafez: Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf 32952, Egypt

Mathematics, 2016, vol. 4, issue 1, 1-12

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.

Keywords: forced duffing oscillator; forced van der Pol Oscillator; Padé approximant; laplace transform; semi-analytical solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2016
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