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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
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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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