Numerical methods for the variable-order fractional advection-diffusion equation with a nonlinear source term
Zhuang, P., Liu, F., Anh, V., & Turner, I. W. (2009) Numerical methods for the variable-order fractional advection-diffusion equation with a nonlinear source term. SIAM Journal on Numerical Analysis (SINUM), 47(3), pp. 1760-1781.
In this paper, we consider a variable-order fractional advection-diffusion equation with a nonlinear source term on a finite domain. Explicit and implicit Euler approximations for the equation are proposed. Stability and convergence of the methods are discussed. Moreover, we also present a fractional method of lines, a matrix transfer technique, and an extrapolation method for the equation. Some numerical examples are given, and the results demonstrate the effectiveness of theoretical analysis.
Impact and interest:
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:||fractional derivative of variable order, nonlinear fractional advection-diffusion equation, finite difference methods, method of lines, extrapolation method, stability and convergence|
|Subjects:||Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200)|
|Divisions:||Past > QUT Faculties & Divisions > Faculty of Science and Technology|
Past > Schools > Mathematical Sciences
|Copyright Owner:||Copyright 2009 Society for Industrial and Applied Mathematics|
|Deposited On:||19 Jan 2010 08:10|
|Last Modified:||01 Mar 2012 00:04|
Repository Staff Only: item control page