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

Author

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  • H. M. Abdelhafez

    (Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf 32952, Egypt)

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.

Suggested Citation

  • H. M. Abdelhafez, 2016. "Solution of Excited Non-Linear Oscillators under Damping Effects Using the Modified Differential Transform Method," Mathematics, MDPI, vol. 4(1), pages 1-12, March.
    • Handle: RePEc:gam:jmathe:v:4:y:2016:i:1:p:11-:d:64936
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    References listed on IDEAS

    as
    1. Kangalgil, Figen & Ayaz, Fatma, 2009. "Solitary wave solutions for the KdV and mKdV equations by differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 464-472.
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