WoS İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12573/394

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  • Article
    Citation - WoS: 26
    Citation - Scopus: 33
    Solitary-Wave Solutions of the GRLW Equation Using Septic B-Spline Collocation Method
    (Elsevier Science inc, 2016-10) 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.
  • Article
    Citation - WoS: 8
    Citation - Scopus: 10
    A Septic B-Spline Collocation Method for Solving the Generalized Equal Width Wave Equation
    (Elsevier, 2016) Karakoc, Seydi B. G.; Zeybek, Halil
    In 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: 24
    Citation - Scopus: 27
    A 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 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.