Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2014, Special Issue (2014), Article ID 653797, 17 pages.
High-Order Algorithms for Riesz Derivative and Their Applications
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.
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