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

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Author: search.filters.author.Zeybek, HalilSubject: search.filters.subject.GRLW Equation

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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: 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.