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Turkish Journal of Mathematics

MELİKE KARTA

DOI

10.55730/1300-0098.3377

Abstract

In the present manuscript, the Benjamin-Bona-Mahony-Burgers (BBMB) equation will be handled numerically by Strang time-splitting technique. While applying this technique, collocation method based on quintic B-spline basis functions is applied. In line with our purpose, after splitting the BBM-Burgers equation given with appropriate initial boundary conditions into two subequations containing the derivative in terms of time, the quintic B-spline based collocation finite element method (FEM) for spatial discretization and the suitable finite difference approaches for time discretization is applied to each subequation and hereby two different systems of algebraic equations are obtained. Four test problems are utilized to test the efficiency and reliability of the presented method. The error norms $L_2$ and $L_\infty$ with mass, energy, and momentum conservation constants $I_1$,$I_2$ and $I_3$, respectively, are computed. To do a comparison with the other studies in the literature, the newly found approximate solutions are exhibited in both tabular and graphical formats. Also, stability analysis of numerical approach by the von Neumann method is researched.

Keywords

BBMB equation, quintic B-splines, collocation method, Strang splitting

First Page

537

Last Page

553

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