Numerical algorithms for time-fractional subdiffusion equation with second-order accuracy

Zeng, Fanhai, Li, Changpin, Liu, Fawang, & Turner, Ian (2015) Numerical algorithms for time-fractional subdiffusion equation with second-order accuracy. SIAM Journal on Scientific Computing, 37(1), A55-A78.

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This article aims to fill in the gap of the second-order accurate schemes for the time-fractional subdiffusion equation with unconditional stability. Two fully discrete schemes are first proposed for the time-fractional subdiffusion equation with space discretized by finite element and time discretized by the fractional linear multistep methods. These two methods are unconditionally stable with maximum global convergence order of $O(\tau+h^{r+1})$ in the $L^2$ norm, where $\tau$ and $h$ are the step sizes in time and space, respectively, and $r$ is the degree of the piecewise polynomial space. The average convergence rates for the two methods in time are also investigated, which shows that the average convergence rates of the two methods are $O(\tau^{1.5}+h^{r+1})$. Furthermore, two improved algorithms are constrcted, they are also unconditionally stable and convergent of order $O(\tau^2+h^{r+1})$. Numerical examples are provided to verify the theoretical analysis. The comparisons between the present algorithms and the existing ones are included, which show that our numerical algorithms exhibit better performances than the known ones.

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18 citations in Scopus
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16 citations in Web of Science®

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ID Code: 82650
Item Type: Journal Article
Refereed: Yes
Keywords: finite element method, fractional linear multistep method, fractional derivative, subdiffusion, unconditional stability, convergence
DOI: 10.1137/14096390X
ISSN: 1095-7197
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Dynamical Systems in Applications (010204)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Analysis (010301)
Divisions: Current > Research Centres > ARC Centre of Excellence for Mathematical & Statistical Frontiers (ACEMS)
Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2015 Society for Industrial and Applied Mathematics
Deposited On: 22 Mar 2015 23:09
Last Modified: 12 Aug 2015 10:34

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