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Numerical algorithms for the time‐Caputo and space‐Riesz fractional Bloch‐Torrey equations
Author(s) -
Ding Hengfei,
Li Changpin
Publication year - 2020
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22451
Subject(s) - mathematics , fractional calculus , convergence (economics) , operator (biology) , stability (learning theory) , space (punctuation) , order (exchange) , mathematical analysis , biochemistry , chemistry , linguistics , philosophy , finance , repressor , machine learning , computer science , transcription factor , economics , gene , economic growth
In this paper, high‐order numerical methods for time‐Caputo and space‐Riesz fractional Bloch‐Torrey equations in one‐ and two‐dimensional space are constructed, where the second‐order backward fractional difference operator and the sixth‐order fractional‐compact difference operator are applied to approximate the time and space fractional derivatives, respectively. The stability and convergence of the methods are analyzed and it is shown that the convergence orders are higher than the earlier work. Finally, some numerical experiments are presented to demonstrate the effectiveness of the methods and confirm our theoretical results.