High-Order Algorithms for Riesz Derivative and Their Applications (I)‎

Abstract EN

We firstly develop the high-order numerical algorithms forthe left and right Riemann-Liouville derivatives.

Using these derived schemes,we can get high-order algorithms for the Riesz fractional derivative.

Based onthe approximate algorithm, we construct the numerical scheme for the spaceRiesz fractional diffusion equation, where a fourth-order scheme is proposedfor the spacial Riesz derivative, and where a compact difference scheme isapplied to approximating the first-order time derivative.

It is shown that thedifference scheme is unconditionally stable and convergent.

Finally, numericalexamples are provided which are in line with the theoretical analysis.