An approximation scheme for the time fractional convection-diffusion equation

In this paper, a discrete form is proposed for solving time fractional convection-diffusion equation. Firstly, we obtain a time discrete scheme based on finite difference method. Secondly, we prove that the time discrete scheme is unconditionally stable, and the numerical solution converges to the exact one with order O(τ2−α), where τ is the time step size. Finally, two numerical examples are proposed respectively, to verify the order of convergence.