Numerical solution of time-fractional Benjamin-Bona-Mahony-Burgers equation via finite integration method by using Chebyshev expansion

The finite integration method using Chebyshev polynomial (FIM-CBS) has been proposed in order to overcome the difficulty of solving linear partial differential equations. In this paper, we develop the FIM-CBS in order to devise a powerful numerical algorithm for finding approximate solutions of the nonlinear time-fractional Benjamin-Bona-Mahony-Burgers equations with the initial and boundary conditions. The time-fractional derivative is in the Caputo sense which is estimated by the forward difference quotient. Furthermore, we implement our proposed algorithm via several numerical experiments by comparing the approximate results obtained by our method and other methods with their analytical solutions. It can be evidence that the developed FIM-CBS algorithm is very effective and efficient with a small number of computational grid points which is discretized by the zeros of Chebyshev polynomial of a certain degree