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    A new approach on numerical solutions of the Improved Boussinesq type equation using quadratic B-spline Galerkin finite element method
    (Elsevier Science Inc, 2015) Ucar, Y.; Karaagac, B.; Esen, A.
    In the present manuscript, some numerical solutions of an Improved Boussinesq type equation are obtained by means of quadratic B-spline Galerkin finite element method. Then, error norms L-2 and L-infinity have been calculated to test the accuracy of the current method. In the manuscript, solitary wave movement and interaction of solitary-antisolitary waves are considered as test problems. (C) 2015 Elsevier Inc. All rights reserved.
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    A Numerical Approach to the Rosenau-KdV equation using Galerkin Cubic Finite Element Method
    (Centre Environment Social & Economic Research Publ-Ceser, 2017) Ucar, Y.; Karaagac, B.; Kutluay, S.
    In this paper, a Galerkin finite element method has been used to solve numerically the Rosenau-KdV equation using cubic B-spline functions. The system of ordinary differential equations obtained in terms of element parameters by the application of the method has been solved by using the fourth order Runge-Kutta method. The error norms L-2 and L-infinity together with invariants I-1 and I-2 have been calculated to show the accuracy and efficiency of the method. The computed results have been compared with exact values and also other numerical results available in the literature.
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    A Trigonometric Quintic B-Spline Basis Collocation Method for the KdV-Kawahara Equation
    (Siberian Branch Russian Acad Sciences, 2023) Karaagac, B.; Esen, A.; Owolabi, K. M.; Pindza, E.
    This paper considers an effective numerical collocation method for numerical solution of the KdV-Kawahara equation. This numerical method relies on a finite element formulation and spline interpolation with a trigonometric quintic B-spline basis. First, the KdV-Kawahara equation is reduced to a coupled equation via an auxiliary variable of the form v = u(xxx). The collocation method is then applied to the coupled equation together with the forward difference and the Crank-Nicholson formula. This results in a systemof algebraic equations in terms of time variables with the trigonometric quintic B-spline basis. For determination of the error between the numerical and exact solutions, the error norms L-2 and L-infinity are calculated. The results are illustrated by two numerical examples with their graphical representation and comparison with other methods.