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A novel high-order algorithm for the numerical estimation of fractional differential equations

Asl, Mohammad S.
; 
Javidi, Mohammad
; 
Yan, Yubin
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Affiliation
University of Tabriz; University of Chester
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Publication Date
2018-01-09
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Mathematics
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Abstract
This paper uses polynomial interpolation to design a novel high-order algorithm for the numerical estimation of fractional differential equations. The Riemann-Liouville fractional derivative is expressed by using the Hadamard finite-part integral and the piecewise cubic interpolation polynomial is utilized to approximate the integral. The detailed error analysis is presented and it is established that the convergence order of the algorithm is O(h4−a). Asymptotic expansion of the error for the presented algorithm is also investigated. Some numerical examples are provided and compared with the exact solution to show that the numerical results are in well agreement with the theoretical ones and also to illustrate the accuracy and efficiency of the proposed algorithm.
Citation
Asl, M. S., Javidi, M., & Yan, Y. (2018). A novel high-order algorithm for the numerical estimation of fractional differential equations. Journal of Computational and Applied Mathematics, 342, 180-201. https://doi.org/10.1016/j.cam.2017.12.047
Publisher
Elsevier
Journal
Journal of Computational and Applied Mathematics
Research Unit
URI
http://hdl.handle.net/10034/620809
DOI
10.1016/j.cam.2017.12.047
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PubMed Central ID
Type
Article
Language
en
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ISSN
EISSN
1879-1778
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http://www.sciencedirect.com/science/article/pii/S0377042718300153?via%3Dihub