Browsing by Author "Ak, Turgut"

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    Article
    An Efficient Approach to Numerical Study of the MRLW Equation with B-Spline Collocation Method
    (HINDAWI PUBLISHING CORPORATION, 2014) Karakoc, Seydi Battal Gazi; Ak, Turgut; Zeybek, Halil; 0000-0002-4596-0553; AGÜ, Mühendislik Fakültesi, Bilgisayar Mühendisliği Bölümü; Zeybek, Halil
    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.
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    Article
    Numerical solutions of the kawahara equation by the septic B-spline collocation method
    (International Academic Press, 2014) Karakoç, Battal Gazi; Zeybek, Halil; Ak, Turgut; AGÜ; Zeybek, Halil
    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. L2 and L∞ error norms and conserved quantities are given at selected times. The obtained results are found in good agreement with the some recent results.