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Ding, Hengfei; Li, Changpin; Chen, YangQuan

High-order algorithms for Riesz derivative and their applications. I. (English) Zbl 1434.65113

Abstr. Appl. Anal. 2014, Article ID 653797, 17 p. (2014).
Summary: We firstly develop the high-order numerical algorithms for the left and right Riemann-Liouville derivatives. Using these derived schemes, we can get high-order algorithms for the Riesz fractional derivative. Based on the approximate algorithm, we construct the numerical scheme for the space Riesz fractional diffusion equation, where a fourth-order scheme is proposed for the spacial Riesz derivative, and where a compact difference scheme is applied to approximating the first-order time derivative. It is shown that the difference scheme is unconditionally stable and convergent. Finally, numerical examples are provided which are in line with the theoretical analysis.

Cited in 1 Review
Cited in 26 Documents

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35R11 Fractional partial differential equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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\textit{H. Ding} et al., Abstr. Appl. Anal. 2014, Article ID 653797, 17 p. (2014; Zbl 1434.65113)
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References:

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