General matrix transform method for the Riesz space fractional advection-dispersion equations

TL;DR

This paper introduces a high-order finite difference and Pade approximation method for numerically solving Riesz space fractional advection-dispersion equations, with stability analysis and numerical validation.

Contribution

It presents a novel combined finite difference and Pade approximation scheme specifically designed for Riesz fractional equations, including stability analysis and numerical experiments.

Findings

The method achieves high accuracy in numerical solutions.

Stability of the scheme is theoretically confirmed.

Numerical experiments validate the effectiveness of the approach.

Abstract

In this paper, a mixed high order finite difference scheme-Pad\'{e} approximation method is applied to obtain numerical solution of the Riesz fractional advection-dispersion equation. This method is based on the high order finite difference scheme that derived from fractional centered difference and Pad\'{e} approximation method for space and time integration, respectively. The stability analysis of the proposed method is discussed via theoretical matrix analysis. Numerical experiments are carried out to confirm the theoretical results of the proposed method.