Year: 2020
Author: Xu Guo, Yutian Li, Tieyong Zeng
International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 2 : pp. 195–211
Abstract
In this work, we consider a new fractional derivative with nonsingular kernel introduced by Caputo–Fabrizio (CF) and propose a finite difference method for computing the CF fractional derivatives. Based on an iterative technique, we can reduce the computational complexity from $O$($J$2$N$) to $O$($JN$), and the corresponding storage will be cut down from $O$($JN$) to $O$($N$), which makes the computation much more efficient. Besides, by adopting piece-wise Lagrange polynomials of degrees 1, 2, and 3, we derive the second, third, and fourth order discretization formulas respectively. The error analysis and numerical experiments are carefully provided for the validation of the accuracy and efficiency of the presented method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2020-IJNAM-13647
International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 2 : pp. 195–211
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Caputo–Fabrizio derivative fractional differential equations higher order scheme.