An accurate closed-form approximate solution for the quintic Duffing oscillator equation

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Title: An accurate closed-form approximate solution for the quintic Duffing oscillator equation
Authors: Beléndez, Augusto | Bernabeu, Guillermo | Francés, Jorge | Méndez Alcaraz, David Israel | Marini, Stephan
Research Group/s: Holografía y Procesado Óptico
Center, Department or Service: Universidad de Alicante. Departamento de Física, Ingeniería de Sistemas y Teoría de la Señal | Universidad de Alicante. Instituto Universitario de Física Aplicada a las Ciencias y las Tecnologías
Keywords: Nonlinear oscillator | Approximate solutions | Quintic Duffing equation | Chebyshev polynomials
Knowledge Area: Física Aplicada
Date Created: 10-Nov-2009
Issue Date: 24-Apr-2010
Publisher: Elsevier
Citation: BELÉNDEZ VÁZQUEZ, Augusto, et al. "An accurate closed-form approximate solution for the quintic Duffing oscillator equation". Mathematical and Computer Modelling. Vol. 52, Issues 3-4 (Aug. 2010). ISSN 0895-7177, pp. 637-641
Abstract: An accurate closed-form solution for the quintic Duffing equation is obtained using a cubication method. In this method the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a cubic Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude. The replacement of the original nonlinear equation by an approximate cubic Duffing equation allows us to obtain explicit approximate formulas for the frequency and the solution as a function of the complete elliptic integral of the first kind and the Jacobi elliptic function cn, respectively. Excellent agreement of the approximate frequencies and periodic solutions with the exact ones is demonstrated and discussed and the relative error for the approximate frequency is lower than 0.37%.
Sponsor: This work was supported by the “Ministerio de Ciencia e Innovación” of Spain, under project FIS2008-05856-C02-02 and by the “Vicerrectorado de Tecnología e Innovación Educativa” of the University of Alicante, Spain (GITE-09006-UA).
ISSN: 0895-7177 (Print) | 1872-9479 (Online)
DOI: 10.1016/j.mcm.2010.04.010
Language: eng
Type: info:eu-repo/semantics/article
Peer Review: si
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