A numerical solution strategy based on error analysis for time-fractional mobile/immobile transport model

This paper discusses a finite difference/spectral method for numerical solving of fractal mobile/immobile transport (FM/IT) models based on Caputo fractional derivative (C-FD). The proposed method is based on a finite difference scheme in time and a spectral method in space. Stability and convergence of the method are established rigorously, providing the theoretical basis for solving the equation. We prove that the temporal discretization scheme is unconditionally stable. Some numerical experiments illustrate the efficiency and applicability of the proposed approach in the sense of accuracy and convergence ratio.