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 ( τ 2 − α ) , where τ is the time step size. Finally, two numerical examples are proposed respectively, to verify the order of convergence. [ABSTRACT FROM AUTHOR]