Numerical methods of the fractional advection-dispersion equation with Robin boundary condition

Abstract:

In this paper, we study the practical numerical methods to solve the fractional advection-dispersion equation with Robin boundary condition. We propose an implicit finite difference scheme based on the shifted Grünwald formula to discretize Riemann-Liouville fractional derivative. Existence and uniqueness of numerical solutions are derived. It is proved that the implicit finite difference scheme is unconditionally stable and convergent. Finally, numerical simulations show that the method is efficient.

Key words:Fractional advection-dispersion equation; Robin boundary; Implicit finite difference method; Unconditionally stability; Convergence