Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term
Peixian ZhuangF. LiuVo AnhIan TurnerSchool of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Bris-bane, QLD 4001, Australia
2009en
ABI
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. Moveover, 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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