Yazar "Geyikli, Turabi" seçeneğine göre listele

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    Approximation of the KdVB equation by the quintic B-spline differential quadrature method
    (Academic Publication Council, 2015) Bashan, Ali; Karakoc, Seydi Battal Gazi; Geyikli, Turabi
    In this paper, the Korteweg-de Vries-Burgers' (KdVB) equation is solved numerically by a new differential quadrature method based on quintic B-spline functions. The weighting coefficients are obtained by semi-explicit algorithm including an algebraic system with five-band coefficient matrix. The L-2 and L-infinity error norms and lowest three invariants I-1, I-2 and I-3 have computed to compare with some earlier studies. Stability analysis of the method is also given. The obtained numerical results show that the present method performs better than the most of the methods available in the literature.
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    Numerical Solution of the Modified Equal Width Wave Equation
    (Hindawi Ltd, 2012) Karakoc, Seydi Battal Gazi; Geyikli, Turabi
    Numerical solution of the modified equal width wave equation is obtained by using lumped Galerkin method based on cubic B-spline finite element method. Solitary wave motion and interaction of two solitary waves are studied using the proposed method. Accuracy of the proposed method is discussed by computing the numerical conserved laws L-2 and L-infinity error norms. The numerical results are found in good agreement with exact solution. A linear stability analysis of the scheme is also investigated.
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    A NUMERICAL SOLUTION OF THE MODIFIED REGULARIZED LONG WAVE (MRLW) EQUATION USING QUARTIC B-SPLINES
    (Turkic World Mathematical Soc, 2013) Karakoc, S. Battal Gazi; Geyikli, Turabi; Bashan, Ali
    In this paper, a numerical solution of the modified regularized long wave (MRLW) equation is obtained by subdomain finite element method using quartic B-spline functions. Solitary wave motion, interaction of two and three solitary waves and the development of the Maxwellian initial condition into solitary waves are studied using the proposed method. Accuracy and efficiency of the proposed method are tested by calculating the numerical conserved laws and error norms L-2 and L-infinity. The obtained results show that the method is an effective numerical scheme to solve the MRLW equation. In addition, a linear stability analysis of the scheme is found to be unconditionally stable.
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    Petrov-Galerkin finite element method for solving the MRLW equation
    (Springer Heidelberg, 2013) Karakoc, Seydi Battal Gazi; Geyikli, Turabi
    In this article, a Petrov-Galerkin method, in which the element shape functions are cubic and weight functions are quadratic B-splines, is introduced to solve the modified regularized long wave (MRLW) equation. The solitary wave motion, interaction of two and three solitary waves, and development of the Maxwellian initial condition into solitary waves are studied using the proposed method. Accuracy and efficiency of the method are demonstrated by computing the numerical conserved laws and L-2, L-infinity error norms. The computed results show that the present scheme is a successful numerical technique for solving the MRLW equation. A linear stability analysis based on the Fourier method is also investigated.
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    Petrov-Galerkin method with cubic B-splines for solving the MEW equation
    (Belgian Mathematical Soc Triomphe, 2012) Geyikli, Turabi; Karakoc, S. Battal Gazi
    In the present paper, we introduce a numerical solution algorithm based on a Petrov-Galerkin method in which the element shape functions are cubic B-splines and the weight functions quadratic B-splines. The motion of a single solitary wave and interaction of two solitary waves are studied. Accuracy and efficiency of the proposed method are discussed by computing the numerical conserved laws and L-2, L-infinity error norms. The obtained results show that the present method is a remarkably successful numerical technique for solving the modified equal width wave(MEW) equation. A linear stability analysis of the scheme shows that it is unconditionally stable.
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    Two Different Methods for Numerical Solution of the Modified Burgers' Equation
    (Hindawi Ltd, 2014) Karakoc, Seydi Battal Gazi; Bashan, Ali; Geyikli, Turabi
    A numerical solution of the modified Burgers' equation (MBE) is obtained by using quartic B-spline subdomain finite element method (SFEM) over which the nonlinear term is locally linearized and using quartic B-spline differential quadrature (QBDQM) method. The accuracy and efficiency of the methods are discussed by computing L-2 and L-infinity error norms. Comparisons are made with those of some earlier papers. The obtained numerical results show that the methods are effective numerical schemes to solve the MBE. A linear stability analysis, based on the von Neumann scheme, shows the SFEM is unconditionally stable. A rate of convergence analysis is also given for the DQM.