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Numerical simulation of a class of fractional subdiffusion equations via the alternating direction implicit method
Author(s) -
Yao Wenjuan,
Sun Jiebao,
Wu Boying,
Shi Shengzhu
Publication year - 2016
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.22004
Subject(s) - mathematics , discretization , convergence (economics) , norm (philosophy) , stability (learning theory) , alternating direction implicit method , numerical analysis , transformation (genetics) , fractional calculus , partial differential equation , mathematical analysis , finite difference method , computer science , biochemistry , chemistry , machine learning , political science , law , economics , gene , economic growth
In this article, a new numerical technique is proposed for solving the two‐dimensional time fractional subdiffusion equation with nonhomogeneous terms. After a transformation of the original problem, standard central difference approximation is used for the spatial discretization. For the time step, a new fractional alternating direction implicit (FADI) scheme based on the L 1 approximation is considered. This FADI scheme is constructed by adding a small term, so it is different from standard FADI methods. The solvability, unconditional stability and H 1 norm convergence are proved. Finally, numerical examples show the effectiveness and accuracy of our proposed method. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 531–547, 2016