A Numerical Method Combining Cubic Interpolated Propagation and Shifted Grünwald–Letnikov for Fractional Advection–Dispersion Equations

Recent advances in the numerical solution of fractional partial differential equations have yielded promising results. In particular, the Shifted Grünwald–Letnikov (SGL) approach allows for a generalization of the traditional finite difference method to the context of fractional differential equations. However, when combined with the backward finite difference scheme, the SGL method for the fractional advection–dispersion equation can produce spurious results, similar to those observed in its integer‐order counterpart. In this study, a novel method that combines the SGL approach with the Cubic Interpolated Propagation (CIP) denoted as CIP‐SGL scheme is proposed to mitigate numerical dispersion. The accuracy and validity of the proposed method are demonstrated through computational experiments.