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    An application of trigonometric quintic b-spline collocation method for sawada- kotera equation
    (Adiyaman University, 2022) Karabenli H.; Esen A.; Yağmurlu N.M.
    In this paper, we deal with the numerical solution of Sawada-Kotera (SK) equation classified as the type of fifth order Korteweg-de Vries (gfKdV) equation. In the first step of our study consisting of several steps, nonlinear model problem is split into the system with the coupled new equations by using the transformation wxxx = v. In the second step, to get rid of the nonlinearity of the problem, Rubin-Graves type linearization is used. After these applications, the approximate solutions are obtained by using the trigonometric quintic B-Spline collocation method. The efficiency and accuracy of the present method is demonstrated with the tables and graphs. As it is seen in the tables given with the error nouns L2 and for different time and space steps, the present method is more accurate for the larger element) numbers and smaller time steps. © 2022, Adiyaman University. All rights reserved.
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    Numerical Approximation of the Combined KdV-mKdV Equation via the Quintic B-Spline Differential Quadrature Method
    (Adiyaman University, 2019) Yağmurlu N.M.; Uçar Y.; Başhan A.
    In this paper, quintic B-spline differential quadrature method (QBDQM) has been used to obtain the numerical approximation of the combined Korteweg-de Vries and modified Korteweg-de Vries equation (combined KdV-mKdV). The efficiency and effectiveness of the proposed method has been tested by computing the maximum error norm L? and discrete root mean square error L2 . The newly found numerical approximations have been compared to available numerical approximations and this comparison has shown that the proposed method is an efficient one for solving the combined KdV-mKdV equation. We have also carried out a stability analysis. © 2019, Adiyaman University. All rights reserved.