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.
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Abstract
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.
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| ID Code: | 29755 |
|---|---|
| Item Type: | Journal Article |
| Additional URLs: | |
| Keywords: | fractional derivative of variable order, nonlinear fractional advection-diffusion equation, finite difference methods, method of lines, extrapolation method, stability and convergence |
| DOI: | 10.1137/080730597 |
| ISSN: | 0036-1429 |
| 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 |
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