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Math. Comput. Appl. 2011, 16(3), 761-772; doi:10.3390/mca16030761

Solution of Nonlinear Oscillators with Fractional Nonlinearities by Using the Modified Differential Transformation Method

1
University, Department of Geomatics Engineering, 29100-Gümüşhane, Turkey
2
University, Department of Software Engineering, 29100-Gümüşhane, Turkey
*
Authors to whom correspondence should be addressed.
Published: 1 December 2011
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Abstract

In this paper, an aproximate analytical method called the differential transform method (DTM) is used as a tool to give approximate solutions of nonlinear oscillators with fractional nonlinearites. The differential transformation method is described in a nuthsell. DTM can simply be applied to linear or nonlinear problems and reduces the required computational effort. The proposed scheme is based on the differential transform method (DTM), Laplace transform and Padé approximants. The results to get the differential transformation method (DTM) are applied Padé approximants. The reliability of this method is investigated by comparison with the classical fourth-order Runge–Kutta (RK4) method and Cos-AT and Sine-AT method. Our the presented method showed results to analytical solutions of nonlinear ordinary differential equation. Some plots are gived to shows solutions of nonlinear oscillators with fractional nonlinearites for illustrating the accurately and simplicity of the methods.
Keywords: Padé approximants; Modified differential transform method; Nonlinear oscillators with fractional nonlinearites Padé approximants; Modified differential transform method; Nonlinear oscillators with fractional nonlinearites
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Merdan, M.; Gökdoğan, A. Solution of Nonlinear Oscillators with Fractional Nonlinearities by Using the Modified Differential Transformation Method. Math. Comput. Appl. 2011, 16, 761-772.

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