Yazar "Yagmurlu, Nuri M." seçeneğine göre listele

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    Operator splitting for numerical solution of the modified Burgers' equation using finite element method
    (Wiley, 2019) Ucar, Yusuf; Yagmurlu, Nuri M.; Celikkaya, Ihsan
    The aim of this study is to obtain numerical behavior of a one-dimensional modified Burgers' equation using cubic B-spline collocation finite element method after splitting the equation with Strang splitting technique. Moreover, the Ext4 and Ext6 methods based on Strang splitting and derived from extrapolation have also been applied to the equation. To observe how good and effective this technique is, we have used the well-known the error norms L-2 and in the literature and compared them with previous studies. In addition, the von Neumann (Fourier series) method has been applied after the nonlinear term has been linearized to investigate the stability of the method.
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    Operator time-splitting techniques combined with quintic B-spline collocation method for the generalized Rosenau-KdV equation
    (Wiley, 2019) Kutluay, Selcuk; Karta, Melike; Yagmurlu, Nuri M.
    In this article, the generalized Rosenau-KdV equation is split into two subequations such that one is linear and the other is nonlinear. The resulting subequations with the prescribed initial and boundary conditions are numerically solved by the first order Lie-Trotter and the second-order Strang time-splitting techniques combined with the quintic B-spline collocation by the help of the fourth order Runge-Kutta (RK-4) method. To show the accuracy and reliability of the proposed techniques, two test problems having exact solutions are considered. The computed error norms L-2 and L-infinity with the conservative properties of the discrete mass Q(t) and energy E(t) are compared with those available in the literature. The convergence orders of both techniques have also been calculated. Moreover, the stability analyses of the numerical schemes are investigated.