Numerical algorithm for three-dimensional space fractional advection diffusion equation

Space fractional advection diffusion equations are better to describe anomalous diffusion phenomena because of non-locality of fractional derivatives, which causes people to confront great trouble in problem solving while enjoying the convenience from mathematical modelling, especially in high dimen...

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Bibliographic Details
Published in:IOP conference series. Earth and environmental science 2017-06, Vol.69 (1), p.12127
Main Authors: Hu, Jiahui, Wang, Jungang, Yuan, Zhanbin, Yang, Zongze, Nie, Yufeng
Format: Article
Language:English
Subjects:
Advection
Algorithms
Diffusion
Finite differences
Mathematical analysis
Mathematical models
Numerical analysis
Operators (mathematics)
Predictor-corrector methods
Problem solving
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Summary:Space fractional advection diffusion equations are better to describe anomalous diffusion phenomena because of non-locality of fractional derivatives, which causes people to confront great trouble in problem solving while enjoying the convenience from mathematical modelling, especially in high dimensional cases. In this paper, we solve the three-dimensional problem by the process of dimension by dimension, which can be achieved through a predictor-corrector algorithm. In time discretization, Crank-Nicolson scheme is adopted to match second-order difference operator of the space direction. Then, the efficiency of this method is demonstrated by some numerical examples finally.
ISSN:1755-1307
1755-1315
DOI:10.1088/1755-1315/69/1/012127