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A Fast Implicit Finite Difference Method for Fractional Advection-Dispersion Equations with Fractional Derivative Boundary Conditions

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  • Taohua Liu
  • Muzhou Hou

Abstract

Fractional advection-dispersion equations, as generalizations of classical integer-order advection-dispersion equations, are used to model the transport of passive tracers carried by fluid flow in a porous medium. In this paper, we develop an implicit finite difference method for fractional advection-dispersion equations with fractional derivative boundary conditions. First-order consistency, solvability, unconditional stability, and first-order convergence of the method are proven. Then, we present a fast iterative method for the implicit finite difference scheme, which only requires storage of and computational cost of . Traditionally, the Gaussian elimination method requires storage of and computational cost of . Finally, the accuracy and efficiency of the method are checked with a numerical example.

Suggested Citation

  • Taohua Liu & Muzhou Hou, 2017. "A Fast Implicit Finite Difference Method for Fractional Advection-Dispersion Equations with Fractional Derivative Boundary Conditions," Advances in Mathematical Physics, Hindawi, vol. 2017, pages 1-8, September.
    • Handle: RePEc:hin:jnlamp:8716752
    DOI: 10.1155/2017/8716752
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