Solution for nonlinear Duffing oscillator using variable order variable stepsize block method

Authors

  • Ahmad Fadly Nurullah Rasedee Faculty of Economics and Muamalat, Universiti Sains Islam Malaysia, 71800 Nilai, Negeri Sembilan.
  • Mohamad Hasan Abdul Sathar Centre of Foundation Studies for Agricultural Science, Universiti Putra Malaysia, 43400 Serdang, Selangor.
  • Norizarina Ishak Faculty of Science and Technology, Universiti Sains Islam Malaysia, 71800 Bandar Baru Nilai, Negeri Sembilan.
  • Nur Shuhada Kamarudin Faculty of Economics and Muamalat, Universiti Sains Islam Malaysia, 71800 Bandar Baru Nilai, Negeri Sembilan.
  • Muhamad Azrin Nazri Faculty of Economics and Muamalat, Universiti Sains Islam Malaysia, 71800 Bandar Baru Nilai, Negeri Sembilan.
  • Nur Ainna Ramli Faculty of Economics and Muamalat, Universiti Sains Islam Malaysia, 71800 Bandar Baru Nilai, Negeri Sembilan.
  • Irneza Ismail Faculty of Engineering and Built Environment, Universiti Sains Islam Malaysia, 71800 Bandar Baru Nilai, Negeri Sembilan.
  • Musab Sahrim Faculty of Engineering and Built Environment, Universiti Sains Islam Malaysia, 71800 Bandar Baru Nilai, Negeri Sembilan.

DOI:

https://doi.org/10.11113/matematika.v33.n2.1015

Abstract

Real life phenomena found in various fields such as engineering, physics, biology and communication theory can be modeled as nonlinear higher order ordinary differential equations, particularly the Duffing oscillator. Analytical solutions for these differential equations can be time consuming whereas, conventional numerical solutions may lack accuracy. This research propose a block multistep method integrated with a variable order step size (VOS) algorithm for solving these Duffing oscillators directly. The proposed VOS Block method provides an alternative numerical solution by reducing computational cost (time) but without loss of accuracy. Numerical simulations are compared with known exact solutions for proof of accuracy and against current numerical methods for proof of efficiency (steps taken).

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Published

2017-12-27

How to Cite

Rasedee, A. F. N., Abdul Sathar, M. H., Ishak, N., Kamarudin, N. S., Nazri, M. A., Ramli, N. A., Ismail, I., & Sahrim, M. (2017). Solution for nonlinear Duffing oscillator using variable order variable stepsize block method. MATEMATIKA: Malaysian Journal of Industrial and Applied Mathematics, 33(2), 165–176. https://doi.org/10.11113/matematika.v33.n2.1015

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Articles