An efficient high-order two-level explicit/implicit numerical scheme for two-dimensional time fractional mobile/immobile advection-dispersion model

This article constructs a new two-level explicit/implicit numerical scheme in an approximate solution for the two-dimensional time fractional mobile/immobile advection-dispersion problem. The stability and error estimates of the proposed technique are deeply analyzed in the $L^{\infty }(0,T;L^2)$-norm. The developed approach is less time consuming, fourth-order in space and temporal accurate of order $O\left(k^{2-\frac{\lambda }{2}}\right)$, where $k$ is the time step and $\lambda$ denotes a positive parameter less than 1. This result shows that the two-level explicit/implicit formulation is faster and more efficient than a large class of numerical schemes widely discussed in the literature for the considered problem. Numerical experiments are performed to verify the theoretical studies and to demonstrate the efficiency of the new numerical method.