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Fractional-Compact Numerical Algorithms for Riesz Spatial Fractional Reaction-Dispersion Equations

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Abstract

It is well known that using high-order numerical algorithms to solve fractional differential equations leads to almost the same computational cost with low-order ones but the accuracy (or convergence order) is greatly improved due to the nonlocal properties of fractional operators. Therefore, developing some high-order numerical approximation formulas for fractional derivatives plays a more important role in numerically solving fractional differential equations. This paper focuses on constructing (generalized) high-order fractional-compact numerical approximation formulas for Riesz derivatives. Then we apply the developed formulas to the one- and two-dimension Riesz spatial fractional reaction-dispersion equations. The stability and convergence of the derived numerical algorithms are strictly studied by using the energy analysis method. Finally, numerical simulations are given to demonstrate the efficiency and convergence orders of the presented numerical algorithms.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Tianshui Normal University, Tianshui, 741001, China

    Hengfei Ding

  2. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    Changpin Li

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  1. Hengfei Ding
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  2. Changpin Li
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Correspondence to Hengfei Ding.

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Ding, H., Li, C. Fractional-Compact Numerical Algorithms for Riesz Spatial Fractional Reaction-Dispersion Equations. FCAA 20, 722–764 (2017). https://doi.org/10.1515/fca-2017-0038

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