Variable order variable stepsize algorithm for solving nonlinear Duffing oscillator

• Main Authors: Rasedee, Ahmad Fadly Nurullah, Ishak, Norizarina, Hamzah, Siti Raihana, Ijam, Hazizah Mohd, Suleiman, Mohamed, Ibrahim, Zarina Bibi, Sathar, Mohammad Hasan Abdul, Ramli, Nur Ainna, Kamaruddin, Nur Shuhada
• Format: Article
• Language: English
• Published: Institute of Physics Publishing 2017
• 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

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.