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Implicit finite difference method for fractional percolation equation with Dirichlet and fractional boundary conditions

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Abstract

An implicit finite difference method is developed for a one-dimensional fractional percolation equation (FPE) with the Dirichlet and fractional boundary conditions. The stability and convergence are discussed for two special cases, i.e., a continued seepage flow with a monotone percolation coefficient and a seepage flow with the fractional Neumann boundary condition. The accuracy and efficiency of the method are checked with two numerical examples.

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Author information

Authors and Affiliations

  1. Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China

    Boling Guo & Qiang Xu

  2. School of Mathematical Sciences, Shandong Normal University, Jinan, 250014, China

    Qiang Xu & Zhe Yin

Authors
  1. Boling Guo
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  2. Qiang Xu
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  3. Zhe Yin
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Corresponding author

Correspondence to Qiang Xu.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11171193 and 11371229), the Natural Science Foundation of Shandong Province (No. ZR2014AM033), and the Science and Technology Development Project of Shandong Province (No. 2012GGB01198)

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Guo, B., Xu, Q. & Yin, Z. Implicit finite difference method for fractional percolation equation with Dirichlet and fractional boundary conditions. Appl. Math. Mech.-Engl. Ed. 37, 403–416 (2016). https://doi.org/10.1007/s10483-016-2036-6

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  • DOI: https://doi.org/10.1007/s10483-016-2036-6

Keywords

Chinese Library Classification

2010 Mathematics Subject Classification

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