A Crank-Nicolson type higher order compact exponential scheme for solving variable order time fractional mobile-immobile advection-dispersion model

Abstract

This paper gives the construction and analysis of a new numerical method to solve variable order time fractional mobile-immobile transport model. The proposed numerical method is based on Crank-Nicolson approach with fourth order accurate compact exponential scheme for spatial discretization. We prove that the new scheme is uniquely solvable and unconditionally stable. Furthermore, some numerical results are presented to check the e ectiveness of the proposed scheme and consistency of computational results with the theoretical ndings.