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.
"Fourth-Order Compact Difference Schemes for the Riemann-Liouville and Riesz Derivatives." Abstr. Appl. Anal. 2014 (SI40) 1 - 4, 2014. https://doi.org/10.1155/2014/540692