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 "Collocation method"

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    Article
    A septic B-spline collocation method for solving the generalized equal width wave equation
    (ACADEMIC PUBLICATION COUNCIL, 2016) Karakoc, Seydi B. G.; Zeybek, Halil; AGÜ; 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 L2 and L∞ and the invariants I1, I2 and I3. 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.
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    Article
    Solitary-wave solutions of the GRLW equation using septic B-spline collocation method
    (ELSEVIER SCIENCE INC, 2016) Karakoc, Seydi; Zeybek, Halil; AGÜ; 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 L2 and L∞ and the invariants I1, I2 and I3. 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.