Variable order variable stepsize algorithm for solving nonlinear Duffing oscillator

Nonlinear phenomena in science and engineering such as a periodically forced oscillator with nonlinear elasticity are often modeled by the Duffing oscillator (Duffing equation). The Duffling oscillator is a type of nonlinear higher order differential equation. In this research, a numerical approxima...

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Bibliographic Details
Published in:Journal of physics. Conference series 2017-09, Vol.890 (1), p.12045
Main Authors: Nurullah Rasedee, Ahmad Fadly, Ishak, Norizarina, Hamzah, Siti Raihana, Ijam, Hazizah Mohd, Suleiman, Mohamed, Ibrahim, Zarina Bibi, Abdul Sathar, Mohammad Hasan, Ramli, Nur Ainna, Kamaruddin, Nur Shuhada
Format: Article
Language:English
Subjects:
Accuracy
Algorithms
Differential equations
Duffing equation
Duffing oscillators
Mathematical analysis
Nonlinear phenomena
Physics
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Summary:Nonlinear phenomena in science and engineering such as a periodically forced oscillator with nonlinear elasticity are often modeled by the Duffing oscillator (Duffing equation). The Duffling oscillator is a type of nonlinear higher order differential equation. In this research, a numerical approximation for solving the Duffing oscillator directly is introduced using a variable order stepsize (VOS) algorithm coupled with a backward difference formulation. By selecting the appropriate restrictions, the VOS algorithm provides a cost efficient computational code without affecting its accuracy. Numerical results have demonstrated the advantages of a variable order stepsize algorithm over conventional methods in terms of total steps and accuracy.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/890/1/012045