Determination of Coefficients of High-Order Schemes for Riemann-Liouville Derivative
Joint Authors
Li, Changpin
Wu, Rifang
Ding, Hengfei
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-21, 21 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-04-15
Country of Publication
Egypt
No. of Pages
21
Main Subjects
Medicine
Information Technology and Computer Science
Abstract EN
Although there have existed some numerical algorithms for the fractional differential equations, developing high-order methods (i.e., with convergence order greater than or equal to 2) is just the beginning.
Lubich has ever proposed the high-order schemes when he studied the fractional linear multistep methods, where he constructed the p th order schemes ( p = 2 , 3 , 4 , 5 , 6 ) for the α th order Riemann-Liouville integral and α th order Riemann-Liouville derivative.
In this paper, we study such a problem and develop recursion formulas to compute these coefficients in the higher-order schemes.
The coefficients of higher-order schemes ( p = 7,8 , 9,10 ) are also obtained.
We first find that these coefficients are oscillatory, which is similar to Runge’s phenomenon.
So, they are not suitable for numerical calculations.
Finally, several numerical examples are implemented to testify the efficiency of the numerical schemes for p = 3 , … , 6 .
American Psychological Association (APA)
Wu, Rifang& Ding, Hengfei& Li, Changpin. 2014. Determination of Coefficients of High-Order Schemes for Riemann-Liouville Derivative. The Scientific World Journal،Vol. 2014, no. 2014, pp.1-21.
https://search.emarefa.net/detail/BIM-1049478
Modern Language Association (MLA)
Wu, Rifang…[et al.]. Determination of Coefficients of High-Order Schemes for Riemann-Liouville Derivative. The Scientific World Journal No. 2014 (2014), pp.1-21.
https://search.emarefa.net/detail/BIM-1049478
American Medical Association (AMA)
Wu, Rifang& Ding, Hengfei& Li, Changpin. Determination of Coefficients of High-Order Schemes for Riemann-Liouville Derivative. The Scientific World Journal. 2014. Vol. 2014, no. 2014, pp.1-21.
https://search.emarefa.net/detail/BIM-1049478
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1049478