Numerical solutions to a BBM‐Burgers model with a nonlocal viscous term

Abstract

In this paper, we numerically investigate the BBM‐Burgers equation with a nonlocal viscous term u t + u x − β u t x x + ν π ∂ ∂ t ∫ 0 t u false( s false) t − s d s + γ u u x = α u x x , where 1 π ∂ ∂ t ∫ 0 t u false( s false) t − s d s is the Riemann‐Liouville half derivative. In particular, we implement different numerical schemes to approximate the solution and its asymptotical behavior. Also, we compare our numerical results with those given in for similar models.