Browsing by Author "Karakoc, S. Battal Gazi"

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    APPLICATION OF THE COLLOCATION METHOD WITH B-SPLINES TO THE GEW EQUATION
    (KENT STATE UNIVERSITYETNA, DEPT MATHEMATICS & COMPUTER SCIENCE, KENT, OH 44242-0001, 2017) Zeybek, Halil; Karakoc, S. Battal Gazi; AGÜ, Mühendislik Fakültesi, Bilgisayar Mühendisliği Bölümü
    In this paper, the generalized equal width (GEW) wave equation is solved numerically by using a quintic B-spline collocation algorithm with two different linearization techniques. Also, a linear stability analysis of the numerical scheme based on the von Neumann method is investigated. The numerical algorithm is applied to three test problems consisting of a single solitary wave, the interaction of two solitary waves, and a Maxwellian initial condition. In order to determine the performance of the numerical method, we compute the error in the L-2- and L-infinity- norms and in the invariants I-1, I-2, and I-3 of the GEW equation. These calculations are compared with earlier studies. Afterwards, the motion of solitary waves according to different parameters is designed.
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    A collocation algorithm based on quintic B-splines for the solitary wave simulation of the GRLW equation
    (SHARIF UNIV TECHNOLOGY, PO BOX 11155-8639, TEHRAN, 00000, IRAN, 2019) Zeybek, H.; Karakoc, S. Battal Gazi; AGÜ, Mühendislik Fakültesi, Bilgisayar Mühendisliği Bölümü
    In this article, a collocation algorithm based on quintic B-splines is proposed to find a numerical solution to the nonlinear Generalized Regularized Long Wave (GRLW) equation. Moreover, to analyze the linear stability of the numerical scheme, the von-Neumann technique is used. The numerical approach to three test examples consisting of a single solitary wave, the collision of two solitary waves, and the growth of an undular bore is discussed. The accuracy of the method is demonstrated by calculating the error in L-2 and L-infinity norms and the conservative quantities l(1) , l(2) and l(3). The findings are compared with those previously reported in the literature. Finally, the motion of solitary waves is graphically plotted according to different parameters. (C) 2019 Sharif University of Technology. All rights reserved.