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ADI-Euler and extrapolation methods for the two-dimensional fractional advection-dispersion equation

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Abstract

In this paper, a two-dimensional fractional advection-dispersion equation (2D-FADE) with variable coefficients on a finite domain is considered. We use a new technique of combination of the Alternating Directions Implicit-Euler method (ADI-Euler), the unshifted Grünwald formula for the advection term, the right-shifted Grünwald formula for the diffusion term, and a Richardson extrapolation to establish an unconditionally stable second order accurate difference method. Stability, consistency and convergence of the ADI-Euler method for 2D-FADE are examined. A numerical example with known exact solution is also presented, and the behavior of the error is analyzed to verify the order of convergence of the ADI-Euler method and the extrapolated ADI-Euler method.

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Authors and Affiliations

  1. School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld. 4001, Australia

    F. Liu

  2. Department of Mathematical Sciences, Xiamen University, Xiamen, 361005, China

    F. Liu

  3. Department of Mathematics, Quanzhou Normal University, Quanzhou, 362000, China

    S. Chen

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  1. S. Chen
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  2. F. Liu
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Correspondence to F. Liu.

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Chen, S., Liu, F. ADI-Euler and extrapolation methods for the two-dimensional fractional advection-dispersion equation. J. Appl. Math. Comput. 26, 295–311 (2008). https://doi.org/10.1007/s12190-007-0013-4

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  • DOI: https://doi.org/10.1007/s12190-007-0013-4

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