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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.

MSC:

65D25 Numerical differentiation
26A33 Fractional derivatives and integrals

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References:

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