A Crank-Nicolson difference scheme for the time variable fractional mobile-immobile advection-dispersion equation

A Crank-Nicolson finite difference scheme to solve a time variable order fractional mobile-immobile advection-dispersion equation is introduced and analyzed. Some a priori estimates of discrete L-2-norm with order of convergence O(tau + h(2)) are established on uniform grids where tau and h are the steps sizes in time and space. Stability and convergence of the numerical solutions are presented in detail. Numerical examples are provided to verify the theoretical analysis.