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Error estimates of a high order numerical method for solving linear fractional differential equations.
- Source :
-
Applied Numerical Mathematics . Apr2017, Vol. 114, p201-220. 20p. - Publication Year :
- 2017
-
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 ( Δ t 2 − α ) , 0 < α < 1 , where α is the order of the fractional derivative and Δ t is the step size. We then use a similar idea to prove the error estimates of the 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 ( Δ t 3 − α ) , 0 < α < 1 . Numerical examples are given to show that the numerical results are consistent with the theoretical results. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01689274
- Volume :
- 114
- Database :
- Academic Search Index
- Journal :
- Applied Numerical Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 120984775
- Full Text :
- https://doi.org/10.1016/j.apnum.2016.04.010