Application of a modified He’s homotopy perturbation method to obtain higher-order approximations to a nonlinear oscillator with discontinuities
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Title: | Application of a modified He’s homotopy perturbation method to obtain higher-order approximations to a nonlinear oscillator with discontinuities |
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Authors: | Beléndez, Augusto | Pascual, Carolina | Ortuño, Manuel | Beléndez, Tarsicio | Gallego, Sergi |
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 oscillators | Analytical approximate solutions | Homotopy perturbation method |
Knowledge Area: | Física Aplicada |
Date Created: | 4-Oct-2007 |
Issue Date: | Apr-2009 |
Publisher: | Elsevier |
Citation: | BELÉNDEZ VÁZQUEZ, Augusto, et al. "Application of a modified He’s homotopy perturbation method to obtain higher-order approximations to a nonlinear oscillator with discontinuities". Nonlinear Analysis: Real World Applications. Vol. 10, Issue 2 (Apr. 2009). ISSN 1468-1218, pp. 601-610 |
Abstract: | A modified He’s homotopy perturbation method is used to calculate the periodic solutions of a nonlinear oscillator with discontinuities for which the elastic force term is proportional to sgn(x). The He’s homotopy perturbation method is modified by truncating the infinite series corresponding to the first-order approximate solution before introducing this solution in the second order linear differential equation. We find this modified 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 1.6% for all values of oscillation amplitude, while this relative error is 0.65% for the second iteration and 0.24% when the third-order approximation is considered. Comparison of the result obtained using this method with the exact ones reveals that this modified method 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 the “Generalitat Valenciana”, Spain, under project ACOMP/ 2007/020. |
URI: | http://hdl.handle.net/10045/9183 |
ISSN: | 1468-1218 |
DOI: | 10.1016/j.nonrwa.2007.10.015 |
Language: | eng |
Type: | info:eu-repo/semantics/article |
Peer Review: | si |
Publisher version: | http://dx.doi.org/10.1016/j.nonrwa.2007.10.015 |
Appears in Collections: | INV - GHPO - Artículos de Revistas INV - GMECA - Artículos de Revistas |
Files in This Item:
File | Description | Size | Format | |
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NONRWA_v10_n2_p601_2009.pdf | Versión revisada (acceso libre) | 3,24 MB | Adobe PDF | Open Preview |
NONRWA_v10_n2_p601_2009def.pdf | Versión final (acceso restringido) | 547,79 kB | Adobe PDF | Open Request a copy |
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