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Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term
2009
SIAM Journal on Numerical Analysis
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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.
doi:10.1137/080730597
fatcat:bwqipsk5bzdfvgc4sardm7ovgy