ADYU J SCI Adıyaman University Journal of Science 2147-1630 2146-586X Adıyaman University 10.37094/adyujsci.1156498 Mathematical Sciences Matematik Applied Mathematics Uygulamalı Matematik An Application of Trigonometric Quintic B-Spline Collocation Method for Sawada-Kotera Equation Nuray Tuncay Kara Science and Art Center https://orcid.org/0000-0003-2201-836X Inonu University https://orcid.org/0000-0002-7927-5941 Inonu University https://orcid.org/0000-0003-1593-0254 12 30 2022 12 2 269 282 08 05 2022 11 26 2022

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 w_xxx=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 norms L_2 and L_∞ for different time and space steps, the present method is more accurate for the larger element numbers and smaller time steps.

Sawada-Kotera Equation Collocation Finite Element Method Trigonometric Quintic B-Spline Rubin-Graves Type Linearization
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