High-order Numerical Methods for Riesz Space Fractional Turbulent Diffusion Equation

TL;DR

This paper develops high-order numerical algorithms for Riesz derivatives, achieving convergence from second to sixth order, and applies them to solve the Riesz space fractional turbulent diffusion equation with supporting numerical validation.

Contribution

The paper introduces new high-order schemes for Riesz derivatives and demonstrates their effectiveness in solving fractional turbulent diffusion equations.

Findings

Convergence orders range from 2nd to 6th.

Numerical experiments confirm theoretical accuracy.

Applicable to fractional turbulent diffusion models.

Abstract

Numerical methods for fractional calculus attract increasing interests due to its wide applications in various fields such as physics, mechanics, etc. In this paper, we focus on constructing high-order algorithms for Riesz derivatives, where the convergence orders cover from the second order to the sixth order. Then we apply the established schemes to the Riesz space fractional turbulent diffusion equation. Numerical experiments are displayed which support the theoretical analysis.