Bilgisayar Bilimleri Fakültesi/Faculty of Computer Sciences

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12573/45

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Browsing Bilgisayar Bilimleri Fakültesi/Faculty of Computer Sciences by Subject "Cubic B-spline"

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    Article
    A cubic B-spline Galerkin approach for the numerical simulation of the GEW equation
    (International Academic Press, 2016) Battal Gazi Karakoç S.; Zeybek, Halil; AGÜ; Zeybek, Halil
    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 L2 and L∞ and the invariants I1, I2 and I3 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.
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    A numerical investigation of the GRLW equation using lumped Galerkin approach with cubic B-spline
    (Springer, 2016) Zeybek, Halil; Karakoç, Battal Gazi; AGÜ; Zeybek, Halil
    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 [Formula: see text] and [Formula: see text] and the conservative quantities [Formula: see text], [Formula: see text] and [Formula: see text] 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.