High-order Numerical Methods for Riesz Space Fractional Turbulent Diffusion Equation
For researchers in fractional calculus, this provides higher-order schemes for a specific equation, but the work is incremental as it extends existing methods.
The paper develops high-order numerical methods (second to sixth order) for Riesz derivatives and applies them to the Riesz space fractional turbulent diffusion equation, with numerical experiments confirming theoretical convergence.
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.