A Conserved Linearization Approach for Solving Nonlinear Oscillation Problems

Authors

Sıla O. Korkut, Department of Engineering Science, Izmir Katip C¸ elebi University, Izmir 35620, TurkeyFollow
Nurcan Gucuyenen Kaymak, Department of Mathematics, Izmir Institute of Technology, Izmir 35430, TurkeyFollow
Gamze Tanoglu, Department of Mathematics, Izmir Institute of Technology, Izmir 35430, TurkeyFollow

Author Country (or Countries)

Turkey

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 Fr´echet 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 Schr¨odinger 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.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/journal/100308

Recommended Citation

O. Korkut, Sıla; Gucuyenen Kaymak, Nurcan; and Tanoglu, Gamze (2018) "A Conserved Linearization Approach for Solving Nonlinear Oscillation Problems," Applied Mathematics & Information Sciences: Vol. 12: Iss. 3, Article 8.
DOI: http://dx.doi.org/10.18576/journal/100308
Available at: https://digitalcommons.aaru.edu.jo/amis/vol12/iss3/8