  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.
