A Crank–Nicolson linear difference scheme for a BBM equation with a time fractional nonlocal viscous term

In this paper, we construct a Crank–Nicolson linear finite difference scheme for a Benjamin–Bona–Mahony equation with a time fractional nonlocal viscous term. The stability and convergence of the proposed numerical scheme are rigorously derived. Theoretical analysis shows that the numerical scheme is convergent in the order of O(τ3/2+h²) , where τ and h are the time and space step sizes. Two numerical experiments are presented to verify that the theoretical analysis is accurate and to demonstrate that the numerical scheme is effective.