Yazar "Mersin, Mehmet Ali" seçeneğine göre listele

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    An Improved Numerical Solution of Modified Regularized Long Wave Equation by Quartic Trigonometric B-Spline
    (10.1007/s40819-025-01832-x, 2025) Kirli, Emre; Mersin, Mehmet Ali
    This study presents the application of a numerical method specifically designed to solve the Modified Regularized Long Wave equation, a crucial model in the analysis of non-linear wave dynamics. The proposed method employs a Quartic Trigonometric B-spline approach for spatial discretization, which ensures smooth and accurate interpolation across the spatial domain, while temporal integration is conducted using the well-established fourth-order Runge–Kutta (RK4) scheme, known for its stability and precision. To evaluate the performance of the method, it is applied to three test problems: the propagation of a single solitary wave, the interaction between two and three solitary waves. The invariant quantities are computed for all test cases. To ensure the stability of the method, a stability analysis is performed through the computation of eigenvalues. The results demonstrate that the proposed method achieves a high degree of accuracy in preserving the invariant properties and produces minimal error, highlighting its efficiency and reliability.
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    Öğe
    Galerkin methods for the numerical solution of the Schrödinger equation by using trigonometric B-splines
    (University of Miskolc, 2022) Mersin, Mehmet Ali; Irk, D.; Görgülü, M. Zorşahin
    SciVal Topics Funding details Abstract This paper includes four finite element methods which are based on quadratic, cubic, quartic and quintic trigonometric B-spline functions for space discretization and Crank-Nicolson method for time discretization, to be achieved the numerical solution of the Schrödinger equation (SE). The algorithms obtained by different degrees trigonometric B-spline Galerkin methods are new for getting numerical solution of the SE. To see the accuracy of the proposed methods, two numerical experiments are investigated and the comparison of the methods are given in the test problem section.