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  • Küçük Resim
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    A high order accurate hybrid technique for numerical solution of modified equal width equation
    (Elsevier B.V., 2025) Kirli, Emre; Cıkıt, Serpil
    In this present study, a high-order accurate hybrid technique is developed to establish the approximate solution of Modified Equal Width (MEW) equation which is used to define solitary waves. The spatial integration is based on combining the cubic B-spline and a fourth-order compact finite-difference (FOCFD) scheme, while the temporal integration is carried out by using fourth-order Runge–Kutta (RK4) scheme. In present technique, the new approximation for the spatial second derivative is constructed by the FOCFD scheme in which the spatial second derivatives of unknowns can be written in terms of the unknowns themselves and their first derivatives. Hence, the spatial second derivative reaches the accuracy of order four, while it is represented by the accuracy of order two in the standard cubic B-spline. The stability of the suggested technique is discussed by using the concept of eigenvalue. Three test problems are examined to verify the efficiency and applicability of the suggested technique. The computed results are compared with the other numerical results in previous works. The comparisons reveal that the suggested hybrid technique provides better results with high accuracy and minimum computational effort.
  • Küçük Resim
    Öğe
    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.