Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12573/395
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Article Citation - WoS: 25Citation - Scopus: 29A 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.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.