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High-order algorithms for riesz derivative and their applications (IV)

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Abstract

The main goal of this article is to establish a new 4th-order numerical differential formula to approximate Riesz derivatives which is obtained by means of a newly established generating function. Then the derived formula is used to solve the Riesz space fractional advection-dispersion equation. Meanwhile, by the energy method, it is proved that the difference scheme is unconditionally stable and convergent with order 𝓞(τ2 + h4). Finally, several numerical examples are given to show that the numerical convergence orders of the numerical differential formulas and the finite difference scheme are in line with the theoretical analysis.

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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, 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. High-order algorithms for riesz derivative and their applications (IV). FCAA 22, 1537–1560 (2019). https://doi.org/10.1515/fca-2019-0080

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