Fourth-Order Compact Difference Schemes for the Riemann-Liouville and Riesz Derivatives - Yuxin Zhang; Hengfei Ding; Jincai Luo (Abstract and Applied Analysis)
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.