Numerical algorithms for timefractional subdiffusion equation with secondorder accuracy
Zeng, Fanhai, Li, Changpin, Liu, Fawang, & Turner, Ian (2015) Numerical algorithms for timefractional subdiffusion equation with secondorder accuracy. SIAM Journal on Scientific Computing, 37(1), A55A78.

PDF (149kB) 
Abstract
This article aims to fill in the gap of the secondorder accurate schemes for the timefractional subdiffusion equation with unconditional stability. Two fully discrete schemes are first proposed for the timefractional 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.
Impact and interest:
Citation counts are sourced monthly from Scopus and Web of Science® citation databases.
These databases contain citations from different subsets of available publications and different time periods and thus the citation count from each is usually different. Some works are not in either database and no count is displayed. Scopus includes citations from articles published in 1996 onwards, and Web of Science® generally from 1980 onwards.
Citations counts from the Google Scholar™ indexing service can be viewed at the linked Google Scholar™ search.
Fulltext downloads:
Fulltext downloads displays the total number of times this work’s files (e.g., a PDF) have been downloaded from QUT ePrints as well as the number of downloads in the previous 365 days. The count includes downloads for all files if a work has more than one.
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:  10957197 
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 
Export: EndNote  Dublin Core  BibTeX
Repository Staff Only: item control page