Stability and convergence of difference methods for two‐dimensional Riesz space fractional advection‐dispersion equations with delay

Abstract

In this article, the Riesz space fractional advection‐dispersion equations with delay in two‐dimensional (RFADED in 2D) are considered. The Riesz space fractional derivative is approximated with the aid of backward differential formulas method of second order and shifted Grünwald difference operators. We develop the Crank‐Nicolson scheme using the finite difference method for the RFADED in 2D and show that it is conditionally stable and convergent with the accuracy order O(κ2+h2+k2). Finally, some numerical examples are constructed to demonstrate the efficacy and usefulness of the numerical method.