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01-Applied Mathematics & Information Sciences
An International Journal


Volumes > Volume 12 > No. 3


A Conserved Linearization Approach for Solving Nonlinear Oscillation Problems

PP: 537-543
Sıla O. Korkut, Nurcan Gucuyenen Kaymak, Gamze Tanoglu,
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 FrŽechet 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 Schršodinger 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.

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