期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 230, 期 24, 页码 8713-8728出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2011.08.020
关键词
Multidimensional fractional differential equation; ADI scheme; Stability; Convergence; Discrete energy method
资金
- National Natural Science Foundation of China [10871044]
New numerical techniques are presented for the solution of a two-dimensional anomalous sub-diffusion equation with time fractional derivative. In these methods, standard central difference approximation is used for the spatial discretization, and, for the time stepping, two new alternating direction implicit (ADI) schemes based on the L-1 approximation and backward Euler method are considered. The two ADI schemes are constructed by adding two different small terms, which are different from standard ADI methods. The solvability, unconditional stability and H-1 norm convergence are proved. Numerical results are presented to support our theoretical analysis and indicate the efficiency of both methods. (C) 2011 Elsevier Inc. All rights reserved.
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