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.
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|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|
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