## Abstract and Applied Analysis

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

#### Abstract

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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 540692, 4 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412607138

Digital Object Identifier
doi:10.1155/2014/540692

Mathematical Reviews number (MathSciNet)
MR3206799

Zentralblatt MATH identifier
07022586

#### Citation

Zhang, Yuxin; Ding, Hengfei; Luo, Jincai. Fourth-Order Compact Difference Schemes for the Riemann-Liouville and Riesz Derivatives. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 540692, 4 pages. doi:10.1155/2014/540692. https://projecteuclid.org/euclid.aaa/1412607138

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