Higher-order approximate solutions to the relativistic and Duffing-harmonic oscillators by modified He’s homotopy methods
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Título: | Higher-order approximate solutions to the relativistic and Duffing-harmonic oscillators by modified He’s homotopy methods |
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Autor/es: | Beléndez, Augusto | Pascual, Carolina | Fernandez-Varo, Helena | Neipp, Cristian | Beléndez, Tarsicio |
Grupo/s de investigación o GITE: | Holografía y Procesado Óptico |
Centro, Departamento o Servicio: | Universidad de Alicante. Departamento de Física, Ingeniería de Sistemas y Teoría de la Señal | Universidad de Alicante. Departamento de Óptica, Farmacología y Anatomía |
Palabras clave: | Nonlinear oscillators | Relativistic oscillator | Duffing-harmonic oscillator | Approximate solutions | Homotopy perturbation method |
Área/s de conocimiento: | Física Aplicada |
Fecha de creación: | 30-ago-2007 |
Fecha de publicación: | feb-2008 |
Editor: | Institute of Physics Publishing |
Cita bibliográfica: | BELÉNDEZ VÁZQUEZ, Augusto, et al. "Higher-order approximate solutions to the relativistic and Duffing-harmonic oscillators by modified He’s homotopy methods". Physica Scripta. Vol. 77, No. 2, 065004 (14 pp) (2008), ISSN 0031-8949 |
Resumen: | A modified He’s homotopy perturbation method is used to calculate higher-order analytical approximate solutions to the relativistic and Duffing-harmonic oscillators. 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, and so on. 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. The approximate formulas obtained show excellent agreement with the exact solutions, and are valid for small as well as large amplitudes of oscillation, including the limiting cases of amplitude approaching zero and infinity. For the relativistic oscillator, only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate frequency of less than 1.6% for small and large values of oscillation amplitude, while this relative error is 0.65% for two iterations with two harmonics and as low as 0.18% when three harmonics are considered in the second approximation. For the Duffing-harmonic oscillator the relative error is as low as 0.078% when the second approximation is considered. Comparison of the result obtained using this method with those obtained by the harmonic balance methods reveals that the former is very effective and convenient. |
URI: | http://hdl.handle.net/10045/9150 |
ISSN: | 0031-8949 (Print) | 1402-4896 (Online) |
DOI: | 10.1088/0031-8949/77/02/025004 |
Idioma: | eng |
Tipo: | info:eu-repo/semantics/article |
Revisión científica: | si |
Aparece en las colecciones: | INV - GHPO - Artículos de Revistas INV - GMECA - Artículos de Revistas |
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Archivo | Descripción | Tamaño | Formato | |
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PS_v77_n2_art025004_2008.pdf | Versión revisada (acceso libre) | 5,91 MB | Adobe PDF | Abrir Vista previa |
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