Numerical study of the Benjamin-Bona-Mahony-Burgers equation

Résumé

In this paper, the quadratic B-spline collocation method
is implemented to find numerical solution of the
Benjamin-Bona-Mahony-Burgers (BBMB) equation. Applying the
Von-Neumann stability analysis technique, 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 numerical results have been compared with the
exact solution. The numerical solutions show the
efficiency of the method computationally.