Yazar "Kirli, Emre" seçeneğine göre listele

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    A fourth order one step method for numerical solution of good Boussinesq equation
    (Tubitak Scientific & Technological Research Council Turkey, 2021) Kirli, Emre; Irk, Dursun
    In this paper, we investigate the numerical solution of good Boussinesq equation by using the quartic B-spline Galerkin method for space discretization and the fourth order one-step method for time discretization. The proposed numerical scheme is analyzed for truncation error. Four test problems are studied. The accuracy and efficiency are measured by computing error norm L-infinity and the order of convergence for the proposed method. The results of numerical experiments confirm that the proposed method has a higher accuracy.
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    Efficient techniques for numerical solutions of Fisher's equation using B-spline finite element methods
    (Springer Heidelberg, 2023) Kirli, Emre; Irk, Dursun
    This study presents a numerical solution of Fisher's equation. For time integration, Crank- Nicolson and fourth-order one-step implicit schemes are used and for space discretization, quintic B-spline Collocation and quintic B-spline Galerkin methods are employed. The truncation error is analyzed and the stability of the suggested methods is discussed matrix stability analysis. Three examples are studied to compare the present results with existing numerical results by computing error norm L(8 )and the order of convergence. The obtained results show that the proposed methods are satisfactorily efficient in terms of accuracy.
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    High order accurate method for the numerical solution of the second order linear hyperbolic telegraph equation
    (Wiley, 2023) Kirli, Emre; Irk, Dursun; Zorsahin Gorgulu, Melis
    In this study, the Galerkin finite element method is applied to get the numerical solution of the linear telegraph equation by using cubic B-spline function. Differently from the existing studies, the fourth order one-step method is used to discretize in time the telegraph equation. The efficiency and accuracy of the proposed method is studied by three examples. The obtained results are shown that the proposed method has a higher accuracy.