Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term

Liu, F., Yang, C. and Burrage, K. (2009) Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term. Journal of Computational and Applied Mathematics, 231 1: 160-176. doi:10.1016/j.cam.2009.02.013


Author Liu, F.
Yang, C.
Burrage, K.
Title Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term
Journal name Journal of Computational and Applied Mathematics   Check publisher's open access policy
ISSN 0377-0427
Publication date 2009-09
Sub-type Article (original research)
DOI 10.1016/j.cam.2009.02.013
Volume 231
Issue 1
Start page 160
End page 176
Total pages 17
Place of publication Antwerp, Belgium
Publisher Elsevier
Language eng
Abstract In this paper, we consider a modified anomalous subdiffusion equation with a nonlinear source term for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. A new implicit difference method is constructed. The stability and convergence are discussed using a new energy method. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of theoretical analysis.
Formatted abstract
F. Liua, c, Corresponding author contact information, E-mail the corresponding author, E-mail the corresponding author,
C. Yangb,
K. Burragec, d, e

a School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld. 4001, Australia
b School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
c IMB, University of Queensland, Qld. 4072, Australia
d COMLAB, Oxford University, OX1 3LB, UK
e OCISB, Oxford University, OX1 3LB, UK
Keyword Implicit difference method
Modified anomalous subdiffusion equation
Nonlinear source terms
Energy method
Stability and convergence
Q-Index Code C1
Q-Index Status Provisional Code

Document type: Journal Article
Sub-type: Article (original research)
Collections: Excellence in Research Australia (ERA) - Collection
Institute for Molecular Bioscience - Publications
 
Versions
Version Filter Type
Citation counts: TR Web of Science Citation Count  Cited 94 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 102 times in Scopus Article | Citations
Google Scholar Search Google Scholar
Created: Thu, 03 Sep 2009, 07:53:23 EST by Mr Andrew Martlew on behalf of Institute for Molecular Bioscience