WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12573/394
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Article Citation - WoS: 26Citation - Scopus: 33Solitary-Wave Solutions of the GRLW Equation Using Septic B-Spline Collocation Method(Elsevier Science inc, 2016-10) Karakoc, S. Battal Gazi; Zeybek, HalilIn 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.Article Citation - WoS: 20Citation - Scopus: 21Application of the Collocation Method With B-Splines to the GEW Equation(Kent State University, 2017) Zeybek, Halil; Karakoc, S. Battal GaziIn 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.Article Citation - WoS: 8Citation - Scopus: 10A Septic B-Spline Collocation Method for Solving the Generalized Equal Width Wave Equation(Elsevier, 2016) Karakoc, Seydi B. G.; Zeybek, HalilIn this work, a septic B-spline collocation method is implemented to find the numerical solution of the generalized equal width (GEW) wave equation by using two different linearization techniques. Test problems including single soliton, interaction of solitons and Maxwellian initial condition are solved to verify the proposed method by calculating the error norms L-2 and L-8 and the invariants I-1, I-2 and I-3. Applying the Von-Neumann stability analysis, the proposed method is shown to be unconditionally stable. As a result, the obtained results are found in good agreement with the some recent results.Article Citation - WoS: 24Citation - Scopus: 27A Numerical Investigation of the GRLW Equation Using Lumped Galerkin Approach With Cubic B-Spline(Springer International Publishing AG, 2016-02-27) Zeybek, Halil; Karakoc, S. Battal GaziIn 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.