Fourth-Order Compact Difference Schemes for the Riemann-Liouville and Riesz Derivatives

Abstract EN

We propose two new compact difference schemes for numerical approximation of the Riemann-Liouville and Riesz derivatives, respectively.

It is shown that these formulas have fourth-order convergence order by means of the Fourier transform method.

Finally, some numerical examples are implemented to testify the efficiency of the numerical schemes and confirm the convergence orders.