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Applications of Parameter-Expanding Method to Nonlinear Oscillators in which the Restoring Force is Inversely Proportional to the Dependent Variable or in Form of Rational Function of Dependent Variable

Canan Köroğlu1, Turgut Öziş2
Department of Mathematics, Faculty of Science, Hacettepe University, Campus, 06800, Beytepe-Ankara, Turkey, Email: ckoroglu@hu.edu.tr
Department of Mathematics, Faculty of Science, Ege University, Campus, 35100, Bornova-Ýzmir, Turkey, Email: turgut.ozis@ege.edu.tr

Computer Modeling in Engineering & Sciences 2011, 75(3&4), 223-234. https://doi.org/10.3970/cmes.2011.075.223

Abstract

He's parameter-expanding method with an adjustment of restoring forces in terms of Chebyshev's series is used to construct approximate frequency-amplitude relations for a conservative nonlinear singular oscillator in which the restoring force is inversely proportional to the dependent variable or in form of rational function of dependant variable. The procedure is used to solve the nonlinear differential equation approximately. The approximate frequency obtained using this procedure is more accurate than those obtained using other approximate methods and the discrepancy between the approximate frequency and the exact one negligible.

Keywords

Parameter-expanding method, Non-linear oscillator

Cite This Article

Köroğlu, C., Öziş, T. (2011). Applications of Parameter-Expanding Method to Nonlinear Oscillators in which the Restoring Force is Inversely Proportional to the Dependent Variable or in Form of Rational Function of Dependent Variable. CMES-Computer Modeling in Engineering & Sciences, 75(3&4), 223–234.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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