Browsing by Author "Karakoc, S. Battal Gazi"

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Citation - WoS: 20
Citation - Scopus: 21
Application of the Collocation Method With B-Splines to the GEW Equation
(Kent State University, 2017) Zeybek, Halil; Karakoc, S. Battal Gazi
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.
Citation - WoS: 7
Citation - Scopus: 6
A Collocation Algorithm Based on Quintic B-Splines for the Solitary Wave Simulation of the GRLW Equation
(Sharif Univ Technology, 2019) Zeybek, H.; Karakoc, S. Battal Gazi
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.
Citation - WoS: 24
Citation - Scopus: 27
A Numerical Investigation of the GRLW Equation Using Lumped Galerkin Approach With Cubic B-Spline
(Springer International Publishing AG, 2016) Zeybek, Halil; Karakoc, S. Battal Gazi
In this work, we construct the lumped Galerkin approach based on cubic B-splines to obtain the numerical solution of the generalized regularized long wave equation. Applying the von Neumann approximation, it is shown that the linearized algorithm is unconditionally stable. The presented method is implemented to three test problems including single solitary wave, interaction of two solitary waves and development of an undular bore. To prove the performance of the numerical scheme, the error norms L-2 and L-infinity and the conservative quantities I-1, I-2 and I-3 are computed and the computational data are compared with the earlier works. In addition, the motion of solitary waves is described at different time levels.
Citation - WoS: 25
Citation - Scopus: 32
Solitary-Wave Solutions of the GRLW Equation Using Septic B-Spline Collocation Method
(Elsevier Science inc, 2016) Karakoc, S. Battal Gazi; Zeybek, Halil
In this work, solitary-wave solutions of the generalized regularized long wave (GRLW) equation are obtained by using septic B-spline collocation method with two different linearization techniques. To demonstrate the accuracy and efficiency of the numerical scheme, three test problems are studied by calculating the error norms L-2 and L-infinity and the invariants I-1, I-2 and I-3. A linear stability analysis based on the von Neumann method of the numerical scheme is also investigated. Consequently, our findings indicate that our numerical scheme is preferable to some recent numerical schemes. (C) 2016 Elsevier Inc. All rights reserved.