Abstract
Based on characteristic method and shifted Grünwald fractional difference method, a characteristic finite difference method is proposed for solving the one/two/three-dimension spatial-fractional convection-dominated diffusion equation. The resulting schemes are first-order accuracy in time and second-order accuracy in space. For high-dimensional problems, alternating direction implicit (ADI) schemes are further proposed. The stability and convergence properties of these schemes are discussed. Numerical experiments are carried out to support the theoretical analysis, and some comparisons with the implicit upwind finite difference scheme are presented to show the effectiveness of the proposed method.
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