Higher order analytical approximate solutions to the nonlinear pendulum by He's homotopy method

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Title: Higher order analytical approximate solutions to the nonlinear pendulum by He's homotopy method
Authors: Beléndez, Augusto | Pascual, Carolina | Alvarez, Mariela L. | Méndez Alcaraz, David Israel | Yebra Calleja, María Soledad | 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 oscillators | Approximate solutions | Simple pendulum | Homotopy perturbation method
Knowledge Area: Física Aplicada
Date Created: 10-Jul-2008
Issue Date: 19-Dec-2008
Publisher: Institute of Physics Publishing
Citation: BELÉNDEZ VÁZQUEZ, Augusto, et al. "Higher order analytical approximate solutions to the nonlinear pendulum by He's homotopy method". Physica Scripta. Vol. 79, No. 1 (Jan. 2009), 015009 (8pp), ISSN 0031-8949
Abstract: A modified He's homotopy perturbation method is used to calculate the periodic solutions of a nonlinear pendulum. The method has been modified by truncating the infinite series corresponding to the first-order approximate solution and substituting a finite number of terms in the second-order linear differential equation. As can be seen, the modified homotopy perturbation method works very well for high values of the initial amplitude. Excellent agreement of the analytical approximate period with the exact period has been demonstrated not only for small but also for large amplitudes A (the relative error is less than 1% for A < 152°). 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 ‘Generalitat Valenciana’, Spain, under project GVPRE/ 2008/182.
URI: http://hdl.handle.net/10045/9206
ISSN: 0031-8949 (Print) | 1402-4896 (Online)
DOI: 10.1088/0031-8949/79/01/015009
Language: eng
Type: info:eu-repo/semantics/article
Peer Review: si
Appears in Collections:INV - GHPO - Artículos de Revistas
INV - Acústica Aplicada - Artículos de Revistas
INV - GMECA - Artículos de Revistas

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