A linearized second-order finite difference scheme for time fractional generalized BBM equation

In this paper, we consider the generalized Benjamin-Bona-Mahony (BBM) equation with a fractional order derivative in time. By introducing a weighted approach and basing on the L2-1σ formula, a linearized finite difference scheme is proposed to solve the nonlinear problem. The scheme is shown to be unconditionally convergent with second-order in time and space within maximum-norm estimate.