Numerical methods of the fractional advection-dispersion equation with Robin boundary condition
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O241.82

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    Abstract:

    In this paper, we study the practical numerical methods to solve the fractional advection-dispersion equation with Robin boundary condition. We propose an implicit finite difference scheme based on the shifted Grünwald formula to discretize Riemann-Liouville fractional derivative. Existence and uniqueness of numerical solutions are derived. It is proved that the implicit finite difference scheme is unconditionally stable and convergent. Finally, numerical simulations show that the method is efficient.

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Cite this article as: ZENG Bao-Si, YIN Xiu-Cao, XIE Chang-Ping, FANG Shao-Mei. Numerical methods of the fractional advection-dispersion equation with Robin boundary condition [J]. J Sichuan Univ: Nat Sci Ed, 2018, 55: 0013.

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History
  • Received:October 16,2017
  • Revised:November 22,2017
  • Adopted:November 27,2017
  • Online: January 05,2018