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Error estimates of a high order numerical method for solving linear fractional differential equations

Li, Zhiqiang
; 
Yan, Yubin
; 
Ford, Neville J.
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Luliang University; University of Chester
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2016-04-29
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Mathematics
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Abstract
In this paper, we first introduce an alternative proof of the error estimates of the numerical methods for solving linear fractional differential equations proposed in Diethelm [6] where a first-degree compound quadrature formula was used to approximate the Hadamard finite-part integral and the convergence order of the proposed numerical method is O(∆t 2−α ), 0 < α < 1, where α is the order of the fractional derivative and ∆t is the step size. We then use the similar idea to prove the error estimates of a high order numerical method for solving linear fractional differential equations proposed in Yan et al. [37], where a second-degree compound quadrature formula was used to approximate the Hadamard finite-part integral and we show that the convergence order of the numerical method is O(∆t 3−α ), 0 < α < 1. The numerical examples are given to show that the numerical results are consistent with the theoretical results.
Citation
Li, Z., Yan, Y., & Ford, N. J. (2016). Error estimates of a high order numerical method for solving linear fractional differential equations. Applied Numerical Mathematics, 114, 201-220. https://doi.org/10.1016/j.apnum.2016.04.010
Publisher
Elsevier
Journal
Applied Numerical Mathematics
Research Unit
URI
http://hdl.handle.net/10034/609518
DOI
10.1016/j.apnum.2016.04.010
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Type
Article
Language
en
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1873-5460
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http://www.journals.elsevier.com/applied-numerical-mathematics/