Fourth-order compact difference schemes for the Riemann-Liouville and Riesz derivatives. (English) Zbl 1468.65022

Summary: 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.


65D25 Numerical differentiation
26A33 Fractional derivatives and integrals


Full Text: DOI


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