Abstract and Applied Analysis

High-Order Algorithms for Riesz Derivative and Their Applications ( I )

Hengfei Ding, Changpin Li, and YangQuan Chen

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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.

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Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 653797, 17 pages.

First available in Project Euclid: 6 October 2014

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Ding, Hengfei; Li, Changpin; Chen, YangQuan. High-Order Algorithms for Riesz Derivative and Their Applications $(I)$. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 653797, 17 pages. doi:10.1155/2014/653797. https://projecteuclid.org/euclid.aaa/1412606725

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