Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/11147/7148

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Access type: Open accessInstitution Author: search.filters.institutionAuthor.Gücüyenen Kaymak, Nurcan

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  • Article
    Citation - Scopus: 2
    A Conserved Linearization Approach for Solving Nonlinear Oscillation Problems
    (Natural Sciences Publishing, 2018) Korkut, Sıla Övgü; Gücüyenen Kaymak, Nurcan; Tanoğlu, Gamze
    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.
  • Article
    Citation - WoS: 5
    Citation - Scopus: 5
    Convergence Analysis and Numerical Solution of the Benjamin-Bona Equation by Lie-Trotter Splitting
    (TUBITAK, 2018) Zürnacı, Fatma; Gücüyenen Kaymak, Nurcan; Seydaoğlu, Muaz; Tanoğlu, Gamze
    In this paper, an operator splitting method is used to analyze nonlinear Benjamin-Bona-Mahony-type equations. We split the equation into an unbounded linear part and a bounded nonlinear part and then Lie-Trotter splitting is applied to the equation. The local error bounds are obtained by using the approach based on the differential theory of operators in a Banach space and the quadrature error estimates via Lie commutator bounds. The global error estimate is obtained via Lady Windermere's fan argument. Finally, to confirm the expected convergence order, numerical examples are studied.