Numerical solution for Benjamin-Bona-Mahony-Burgers equation with Strang time-splitting technique

In the present manuscript, the Benjamin-Bona-Mahony-Burgers (BBMB) equation will be handled numerically by Strang time-splitting technique based on quintic B-spline collocation method. In line with our purpose, after dividing the BBM-Burgers equation given with appropriate initial boundary conditions into two sub-equations 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 sub-equation and hereby two different systems of algebraic equations are obtained. Four test problems are submited to test the efficiency and reliability of the presented method. The error norms $L_2$ and $L_\infty$ with invariants $I_1$,$I_2$ and $I_3$ 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.