Ampol Duangpan and Ratinan Boonklurb

DOI: 10.14456/sjst-psu.2021.90

pp. 677 - 686

Abstract

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. 

Keywords

• finite integration method
• Chebyshev expansion
• time fractional derivative
• Benjamin-Bona-Mahony-Burgers equation
• Caputo fractional derivative