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Journals / Mathematical and Computational Applications / 2011 / Cilt: 16 - Sayı: 3

Solution of nonlinear oscillators with fractional nonlinearities by using the modified differential transformation method

MEHMET MERDAN
AHMET GÖKDOĞAN
Pages
761–772
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Some plots are gived to shows solutions of nonlinear oscillators with fractional nonlinearites for illustrating the accurately and simplicity of the methods.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
📊
Key Findings & Data: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.
💡
Conclusion & Impact:Some plots are gived to shows solutions of nonlinear oscillators with fractional nonlinearites for illustrating the accurately and simplicity of the methods.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

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.

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Cite This Article

MERDAN, M., GÖKDOĞAN, A. (2011). Solution of nonlinear oscillators with fractional nonlinearities by using the modified differential transformation method. Mathematical and Computational Applications, Cilt: 16 - Sayı: 3, 761–772. https://ajindex.com/articles/280317

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