Publication: Solution for nonlinear Duffing oscillator using variable order variable stepsize block method
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Date
2017
Journal Title
Journal ISSN
Volume Title
Publisher
Penerbit UTM Press
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).
Description
MATEMATIKA, 2017, Volume 33, Number 2, 165–175
Keywords
Duffing Oscillator, multistep method, ordinary differential equations
Citation
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