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    A High Order Accurate Numerical Solution of the Klein-Gordon Equation
    (Natural Sciences Publishing, 2022) Irk, D.; Kirli, E.; Gorgulu, M.Z.
    In this paper, numerical solution of the nonlinear Klein-Gordon equation is obtained by using the cubic B-spline Galerkin method for space discretization and the finite difference method which is of order four for time discretization. Accuracy of the method is presented by computing the maximum error norm. Robustness of the suggested method is shown by studying some classical test problems © 2022. NSP Natural Sciences Publishing Cor
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    NUMERICAL SOLUTION OF SECOND ORDER LINEAR HYPERBOLIC TELEGRAPH EQUATION
    (Turkic World Mathematical Soc, 2022) Kirli, E.; Irk, D.; Gorgulu, M. Zorsahin
    This paper is of about a numerical solution of the second order linear hyperbolic telegraph equation. To solve numerically the second order linear hyperbolic telegraph equation, the cubic B-spline collocation method is used in space discretization and the fourth order one-step method is used in time discretization. By using the fourth order one-step method, it is aimed to obtain a numerical algorithm whose accuracy is higher than the current studies. The efficiency and accuracy of the proposed method is studied by two examples. The obtained results show that the proposed method has higher accuracy as intended.
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    Numerical Solution of the Homogeneous Telegraph Equation by Using Galerkin Finite Element Method
    (Springer, 2020) Irk, D.; Kirli, E.
    In this study, high order numerical solution of one dimensional homogeneous Telegraph equation is presented using quadratic B-spline Galerkin finite element method. In the method, second and fourth order single step methods are used for the time integration. Second order single step method is also known as Crank Nicolson method. The numerical example is studied to illustrate the accuracy and the efficiency of the method. © 2020, Springer Nature Switzerland AG.