Numerical Solution for Riesz Fractional Diffusion Equation via Fractional Centered Difference Scheme

Abstract

In this paper, a mixed matrix transform method with fractional centered difference scheme for solving fractional diffusion equation with Riesz fractional derivative was examined. It was obtained that the numerical scheme was unconditionally stable and feasible using the matrix analysis method. Numerical experiments were, then, carried out to support the theoretical predictions.

High-order numerical method for two-dimensional Riesz space fractional advection-dispersion equation

“…The fractional advection-dispersion equation provides a useful description of chemical and contaminant transport in heterogeneous aquifers [2,4], abnormal mass absorption in solids [22] and densities of plumes in spread proportionally to time-dependent of fractional order [3]. Although there is a plenty of research in one dimensional Riesz space fractional advection-dispersion equation (for example, see [1,8,9,13,14,15,17,21,23,24,28,30]), there are few works in the two dimensional case [6,29,31]. In this research, we numerically solve the general two dimensional Riesz space fractional advection-dispersion equation using modified Crank-Nicolson Alternating Direction Implicit (ADI) method.…”