Approximate solutions of a nonlinear oscillator typified as a mass attached to a stretched elastic wire by the homotopy perturbation method
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http://hdl.handle.net/10045/11912
Títol: | Approximate solutions of a nonlinear oscillator typified as a mass attached to a stretched elastic wire by the homotopy perturbation method |
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Autors: | Beléndez, Augusto | Beléndez, Tarsicio | Neipp, Cristian | Hernández Prados, Antonio | Alvarez, Mariela L. |
Grups d'investigació o GITE: | Holografía y Procesado Óptico |
Centre, Departament o Servei: | 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 |
Paraules clau: | Nonlinear oscillators | Analytical approximate solutions | Homotopy perturbation method |
Àrees de coneixement: | Física Aplicada |
Data de creació: | d’octubre-2006 |
Data de publicació: | de gener-2009 |
Editor: | Elsevier |
Citació bibliogràfica: | BELÉNDEZ VÁZQUEZ, Augusto, et al. "Approximate solutions of a nonlinear oscillator typified as a mass attached to a stretched elastic wire by the homotopy perturbation method". Chaos, Solitons & Fractals. Vol. 39, Issue 2 (30 Jan. 2009). ISSN 0960-0779, pp. 746-764 |
Resum: | The homotopy perturbation method is used to solve the nonlinear differential equation that governs the nonlinear oscillations of a system typified as a mass attached to a stretched elastic wire. The restoring force for this oscillator has an irrational term with a parameter λ that characterizes the system (0 λ 1). For λ = 1 and small values of x, the restoring force does not have a dominant term proportional to x. We find this perturbation method works very well for the whole range of parameters involved, and 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 and the maximal relative error for the approximate frequency is less than 2.2% for small and large values of oscillation amplitude. This error corresponds to λ = 1, while for λ < 1 the relative error is much lower. For example, its value is as low as 0.062% for λ = 0.5. |
Patrocinadors: | 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/10045/11912 |
ISSN: | 0960-0779 (Print) | 1873-2887 (Online) |
DOI: | 10.1016/j.chaos.2007.01.089 |
Idioma: | eng |
Tipus: | info:eu-repo/semantics/article |
Revisió científica: | si |
Versió de l'editor: | http://dx.doi.org/10.1016/j.chaos.2007.01.089 |
Apareix a la col·lecció: | INV - GHPO - Artículos de Revistas |
Arxius per aquest ítem:
Arxiu | Descripció | Tamany | Format | |
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CSF_v39_n2_p746_2009.pdf | Versión final (acceso restringido) | 299,1 kB | Adobe PDF | Obrir Sol·licitar una còpia |
CSF_v39_n2_p746_2009pre.pdf | Versión revisada (acceso libre) | 379,11 kB | Adobe PDF | Obrir Vista prèvia |
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