Numerical simulation of the Riesz fractional diffusion equation with a nonlinear source term
In this paper, A Riesz fractional diffusion equation with a nonlinear source term (RFDE-NST) is considered. This equation is commonly used to model the growth and spreading of biological species. According to the equivalent of the Riemann-Liouville(R-L) and Gr¨unwald-Letnikov(GL) fractional derivative definitions, an implicit difference approximation (IFDA) for the RFDE-NST is derived. We prove the IFDA is unconditionally stable and convergent. In order to evaluate the efficiency of the IFDA, a comparison with a fractional method of lines (FMOL) is used. Finally, two numerical examples are presented to show that the numerical results are in good agreement with our theoretical analysis.
Citation countsare sourced monthly fromand 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 theindexing service can be viewed at the linked Google Scholar™ search.
Full-text downloadsdisplays 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.
|Item Type:||Journal Article|
|Keywords:||Riesz Fractional Derivatives, Implicit Difference Approximation, Nonlinear Source, Stability, Convergence|
|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:||Past > QUT Faculties & Divisions > Faculty of Science and Technology|
|Copyright Owner:||Copyright 2008 Springer|
|Deposited On:||12 Feb 2010 22:50|
|Last Modified:||01 Mar 2012 12:16|
Repository Staff Only: item control page