Numerical simulation and convergence analysis for the time-fractional BBMB equation describing wave phenomena

The aim of this work is to implement an efficient numerical method to tackle the time-fractional Benjamin-Bona-Mohany-Burger equations. The Benjamin-Bona-Mohany-Burger equation is a powerful tool in ocean engineering due to its capability to describe the unidirectional propagation of long waves in specific nonlinear dispersive models. To achieve its numerical solution, we apply the Crank-Nicolson technique in the time variable with exponential B-splines in the space variable. We also analyze the scheme’s stability and convergence. As the exact solution is unknown, the double mesh method is applied to estimate the errors. The numerical simulations validate the theoretical analysis and a comparative analysis exhibits the reliability of the developed technique.