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Abstract and Applied Analysis
Volume 2014, Article ID 540692, 4 pages
Research Article

Fourth-Order Compact Difference Schemes for the Riemann-Liouville and Riesz Derivatives

1School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, China
2Caoba Nine-Year School, Honghe Country, Lixian 742203, China

Received 4 March 2014; Revised 14 April 2014; Accepted 14 April 2014; Published 30 April 2014

Academic Editor: Robert A. Van Gorder

Copyright © 2014 Yuxin Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.