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.

In the present paper, non-linear Fisher’s reaction-diffusion equation is solved numerically by using Strang splitting technique with the help of Galerkin method combined with quadratic B-spline base functions. For this aim, Fisher’s equation is split into two sub-equations with respect to time such that one is linear and the other is nonlinear. Galerkin method using quadratic B-spline finite elements is applied to each sub-equation. To check correctness and reliability of the presented approach, we have realized on three numerical examples and have made a comparison with earlier current studies existing in the literature calculating the error norms $L_{2}$ and $L_{\infty}$. The solutions obtained during the article show that the present method is quite proper for using many partial differential equations in terms of being easy and convenient to computer application.

In the present manuscript, we are going to research a numerical scheme of the nonlinear Benjamin-Bona-Mahony-Burgers (BBMB) equation using the Strang time-splitting technique based on cubic B-spline lumped Galerkin method. In line with our aim, this equation is split into two sub-equations containing the derivative in time direction. Each sub-equations is applied Galerkin finite element method with cubic B-splines and after that the resulting equations are solved with the Strang time-splitting technique. Stability analysis of numerical algorithm is investigated. Five test problems with both exact solution and not is suggested to test the accuracy and reliability of the presented method. The error norms $L_{2}$ and $L_{\infty}$ with three invariants $I_{1},I_{2}$ and $I_{3}$ are computed and compared with existing studies in the literature and the obtained numerical results are displayed in graphics as well as tables. The numerical results obtained with this new approach set light to the solution of nonlinear equations as an effective mathematical tool.