Analytical approximate solutions for the cubic-quintic Duffing oscillator in terms of elementary functions
type: Item
instance of: scholarly article
title: Analytical approximate solutions for the cubic-quintic Duffing oscillator in terms of elementary functions
zbMATH Open document ID: 1251.34002
DOI: 10.1155/2012/286290
author: Xianqiang Yang
published in: Journal of Applied Mathematics
publication date: 2012-11-15T00:00:00Z
review text: Summary: Accurate approximate closed-form solutions for the cubic-quintic Duffing oscillator are obtained in terms of elementary functions. To do this, we use the previous results obtained using a cubication method in which the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a cubic Duffing equation. Explicit approximate solutions are then expressed as a function of the complete elliptic integral of the first kind and the Jacobi elliptic function cn. Then we obtain other approximate expressions for these solutions, which are expressed in terms of elementary functions. To do this, the relationship between the complete elliptic integral of the first kind and the arithmetic-geometric mean is used and the rational harmonic balance method is applied to obtain the periodic solution of the original nonlinear oscillator.
Mathematics Subject Classification ID: 34A05
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 6106166
zbMATH Keywords: approximate closed-form solutions
zbMATH Keywords: cubic-quintic Duffing oscillator
Wikidata QID: Q58906557
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/286290
OpenAlex ID: W2119296315
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description: scientific article; zbMATH DE number 6106166