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  4. Variable order variable stepsize algorithm for solving nonlinear Duffing oscillator
 
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Variable order variable stepsize algorithm for solving nonlinear Duffing oscillator

Date Issued
2017
Author(s)
Rasedee, AFN
Ishak, N
Hamzah, SR
Ijam, HM
Suleiman, M
Ibrahim, ZB
Sathar, MHA
Ramli, NA
Kamaruddin, NS
DOI
10.1088/1742-6596/890/1/012045
Abstract
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.
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