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A Fast Compact Finite Difference Method for Fractional Cattaneo Equation Based on Caputo–Fabrizio Derivative
Joint Authors
Qiao, Haili
Liu, Zhengguang
Cheng, Aijie
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-03-19
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
The Cattaneo equations with Caputo–Fabrizio fractional derivative are investigated.
A compact finite difference scheme of Crank–Nicolson type is presented and analyzed, which is proved to have temporal accuracy of second order and spatial accuracy of fourth order.
Since this derivative is defined with an integral over the whole passed time, conventional direct solvers generally take computational complexity of OMN2 and require memory of OMN, with M and N the number of space steps and time steps, respectively.
We develop a fast evaluation procedure for the Caputo–Fabrizio fractional derivative, by which the computational cost is reduced to OMN operations; meanwhile, only OM memory is required.
In the end, several numerical experiments are carried out to verify the theoretical results and show the applicability of the fast compact difference procedure.
American Psychological Association (APA)
Qiao, Haili& Liu, Zhengguang& Cheng, Aijie. 2020. A Fast Compact Finite Difference Method for Fractional Cattaneo Equation Based on Caputo–Fabrizio Derivative. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-17.
https://search.emarefa.net/detail/BIM-1194677
Modern Language Association (MLA)
Qiao, Haili…[et al.]. A Fast Compact Finite Difference Method for Fractional Cattaneo Equation Based on Caputo–Fabrizio Derivative. Mathematical Problems in Engineering No. 2020 (2020), pp.1-17.
https://search.emarefa.net/detail/BIM-1194677
American Medical Association (AMA)
Qiao, Haili& Liu, Zhengguang& Cheng, Aijie. A Fast Compact Finite Difference Method for Fractional Cattaneo Equation Based on Caputo–Fabrizio Derivative. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-17.
https://search.emarefa.net/detail/BIM-1194677
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1194677