Solution of an anti-symmetric quadratic nonlinear oscillator by a modified He’s homotopy perturbation method

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Title: Solution of an anti-symmetric quadratic nonlinear oscillator by a modified He’s homotopy perturbation method
Authors: Beléndez, Augusto | Pascual, Carolina | Beléndez, Tarsicio | Hernández Prados, Antonio
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
Keywords: Nonlinear oscillator | Analytical approximate solutions | Homotopy perturbation method
Knowledge Area: Física Aplicada | Matemática Aplicada
Date Created: 7-Sep-2007
Issue Date: 5-Oct-2007
Publisher: Elsevier
Citation: BELÉNDEZ VÁZQUEZ, Augusto, et al. "Solution of an anti-symmetric quadratic nonlinear oscillator by a modified He’s homotopy perturbation method". Nonlinear Analysis: Real World Applications. Vol. 10, Issue 1 (Febr. 2009). ISSN 1468-1218, pp. 416-427
Abstract: In this paper He’s homotopy perturbation method has been adapted to calculate higher-order approximate periodic solutions of a nonlinear oscillator with discontinuity for which the elastic force term is anti-symmetric and quadratic term. We find He’s homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate period of less than 0.73% for all values of oscillation amplitude, while this relative error is as low as 0.040% when the second iteration is considered. Comparison of the result obtained using this method with those obtained by harmonic balance method reveals that the former is very effective and convenient.
Sponsor: This work was supported by the “Ministerio de Educación y Ciencia”, Spain, under project FIS2005-05881-C02-02, and by the “Generalitat Valenciana”, Spain, under project ACOMP/2007/020.
URI: http://hdl.handle.net/10045/9204
ISSN: 1468-1218
DOI: 10.1016/j.nonrwa.2007.10.002
Language: eng
Type: info:eu-repo/semantics/article
Peer Review: si
Publisher version: http://dx.doi.org/10.1016/j.nonrwa.2007.10.002
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