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Title: A conserved linearization approach for solving nonlinear oscillation problems
Authors: Korkut, Sıla Övgü
Gücüyenen Kaymak, Nurcan
Tanoğlu, Gamze
Keywords: Conservative scheme
Fréchet derivative
Linearization technique
Newton-Raphson method
Nonlinear oscillations
Publisher: Natural Sciences Publishing
Source: Korkut, S. Ö., Gücüyenen Kaymak, N. and Tanoğlu, G. (2018). A conserved linearization approach for solving nonlinear oscillation problems. Applied Mathematics and Information Sciences, 12(3), 537-543. doi:10.18576/amis/120308
Abstract: Nonlinear oscillation problems are extensively used in engineering and applied sciences. Due to non-availability of the analytic solutions, numerical approaches have been used for these equations. In this study, a numerical method which is based on Newton-Raphson linearization and Fréchet derivative is suggested. The convergence analysis is also studied locally. The present method is tested on three examples: damped oscillator, Van-der Pol equation and Schrödinger equation. It is shown that the obtained solutions via the present method are more accurate than those of the well-known second order Runge-Kutta method. When examining the present method, preservation of characteristic properties of these equations is also considered. The obtained results show that the present method is applicable with respect to the efficiency and the physical compatibility.
ISSN: 1935-0090
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

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