Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12573/395

Browse

Filters

2014 - 20166

Settings

Author: search.filters.author.Zeybek, HalilHas files: Yes

Search Results

Now showing 1 - 6 of 6
  • 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: 28
    Citation - Scopus: 25
    An 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 Gazi
    A 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 - 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.
  • Article
    Citation - Scopus: 32
    Numerical 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 Gazi
    In 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: 25
    A 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.