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 2009-09-01
Sub-type Article (original research)
DOI 10.1016/j.cam.2009.02.013
Open Access Status
Volume 231
Issue 1
Start page 160
End page 176
Total pages 17
Place of publication Antwerp, Belgium
Publisher Elsevier
Language eng
Subject 2605 Computational Mathematics
2604 Applied Mathematics
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
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: Excellence in Research Australia (ERA) - Collection
Institute for Molecular Bioscience - Publications
 
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Created: Thu, 03 Sep 2009, 17:53:23 EST by Mr Andrew Martlew on behalf of Institute for Molecular Bioscience