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2014 High-Order Algorithms for Riesz Derivative and Their Applications ( I )
Hengfei Ding, Changpin Li, YangQuan Chen
Abstr. Appl. Anal. 2014(SI58): 1-17 (2014). DOI: 10.1155/2014/653797


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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Hengfei Ding. Changpin Li. YangQuan Chen. "High-Order Algorithms for Riesz Derivative and Their Applications ( I ) ." Abstr. Appl. Anal. 2014 (SI58) 1 - 17, 2014.


Published: 2014
First available in Project Euclid: 6 October 2014

zbMATH: 07022832
MathSciNet: MR3214445
Digital Object Identifier: 10.1155/2014/653797

Rights: Copyright © 2014 Hindawi

Vol.2014 • No. SI58 • 2014
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