Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 242, Issue -, Pages 103-123Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2013.02.014
Keywords
Fractional derivatives; Reaction-subdiffusion equation; Mixed spline function; Fourier method; Numerical stability
Funding
- Key Program of Shanghai Municipal Education Commission [12ZZ084]
- Shanghai Leading Academic Discipline Project [S30104]
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In this paper, we develop two classes of finite difference schemes for the reaction-subdiffusion equations by using a mixed spline function in space direction, forward and backward difference in time direction, respectively. It has been shown that some of the previous known difference schemes can be derived from our schemes if we suitably choose the spline parameters. By Fourier method, we prove that one class of difference scheme is unconditionally stable and convergent, the other is conditionally stable and convergent. Finally, some numerical results are provided to demonstrate the effectiveness of the proposed difference schemes. (C) 2013 Elsevier Inc. All rights reserved.
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