A stable explicitly solvable numerical method for the Riesz fractional advection–dispersion equations

Jingyuan Zhang

Applied Mathematics and Computation, 2018, vol. 332, issue C, 209-227

Abstract: In this paper, we present a finite difference scheme for solving the Riesz fractional advection-dispersion equations (RFADEs). The scheme is obtained by using asymmetric discretization technique and modify the shifted Grünwald approximation to fractional derivative. By calculating the unknowns in differential nodal-point sequences at the odd and even time-levels, the discrete solution of the scheme can be obtained explicitly. The computational cost for the scheme at each time step can be O(KlogK) by using the fast matrix-vector multiplication with the help of Toeplitz structure, where K is the number of unknowns. We prove that the scheme is solvable and unconditionally stable. We derive the error estimates in discrete l2-norm, which is optimal in some cases. Numerical examples are presented to verify our theoretical results.

Keywords: Riesz fractional advection-dispersion equations; Finite difference scheme; Asymmetric technique; Unconditional stable; Error estimates (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:332:y:2018:i:c:p:209-227

DOI: 10.1016/j.amc.2018.03.060

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