Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12573/395
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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: 28Citation - Scopus: 25An Efficient Approach to Numerical Study of the MRLW Equation With B-Spline Collocation Method(Hindawi Ltd, 2014) Karakoc, Seydi Battal Gazi; Ak, Turgut; Zeybek, Halil; Karakoҫ, Seydi Battal GaziA septic B-spline collocation method is implemented to find the numerical solution of the modified regularized long wave (MRLW) equation. Three test problems including the single soliton and interaction of two and three solitons are studied to validate the proposed method by calculating the error norms L-2 and L-infinity and the invariants I-1, I-2, and I-3. Also, we have studied the Maxwellian initial condition pulse. The numerical results obtained by the method show that the present method is accurate and efficient. Results are compared with some earlier results given in the literature. A linear stability analysis of the method is also investigated.Article Citation - Scopus: 32Numerical Solutions of the Kawahara Equation by the Septic B-Spline Collocation Method(International Academic Press, 2014) Karakoç, Seydi Battal Gazi; Zeybek, Halil; Ak, Turgut; Karakoç, Battal GaziIn this article, a numerical solution of the Kawahara equation is presented by septic B-spline collocation method. Applying the Von-Neumann stability analysis, the present method is shown to be unconditionally stable. The accuracy of the proposed method is checked by two test problems. L<inf>2</inf> and L<inf>∞</inf> error norms and conserved quantities are given at selected times. The obtained results are found in good agreement with the some recent results. © 2016 Elsevier B.V., All rights reserved.Article Citation - Scopus: 25A Cubic B-Spline Galerkin Approach for the Numerical Simulation of the GEW Equation(International Academic Press, 2016) Karakoç, Seydi Battal Gazi; Zeybek, Halil; Battal Gazi Karakoç, S.The generalized equal width (GEW) wave equation is solved numerically by using lumped Galerkin approach with cubic B-spline functions. The proposed numerical scheme is tested by applying two test problems including single solitary wave and interaction of two solitary waves. In order to determine the performance of the algorithm, the error norms L<inf>2</inf> and L<inf>∞</inf> and the invariants I<inf>1</inf>, I<inf>2</inf> and I<inf>3</inf> are calculated. For the linear stability analysis of the numerical algorithm, von Neumann approach is used. As a result, the obtained findings show that the presented numerical scheme is preferable to some recent numerical methods. © 2016 Elsevier B.V., All rights reserved.