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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| Main Authors: | , , , , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Institute of Physics Publishing
2017
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| Online Access: | http://psasir.upm.edu.my/id/eprint/63677/1/Variable%20order%20variable%20stepsize%20algorithm%20for.pdf http://psasir.upm.edu.my/id/eprint/63677/ http://iopscience.iop.org/article/10.1088/1742-6596/890/1/012045/pdf |
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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. |
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