Journal
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume 47, Issue 3, Pages 1760-1781Publisher
SIAM PUBLICATIONS
DOI: 10.1137/080730597
Keywords
fractional derivative of variable order; nonlinear fractional advection-diffusion equation; finite difference methods; method of lines; extrapolation method; stability and convergence
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Funding
- Australian Research Council [DP0559807, DP0986766]
- National Natural Science Foundation of China [10271098]
- NSF of China [10726061]
- Natural Science Foundation of Fujian province [Z0511009]
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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.
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