Error analysis of the numerical solution of the Benjamin-Bona-Mahony-Burgers equation

Abstract

In this paper, the B-spline collocation scheme is implemented to find numerical solution of the nonlinear Benjamin-Bona-Mahony-Burgers equation. The method is based on collocation of quintic B-spline. We show that the method is unconditionally stable. Also the convergence of the method is proved. The method is applied on some test examples, and the numerical results have been compared with the analytical solutions. The $L_\infty$ and $L_2$ in the solutions show the efficiency of the method computationally.