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High-Order Algorithms for Riesz Derivative and their Applications (III)

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Abstract

Numerical methods for fractional calculus attract increasing interest due to its wide applications in various fields such as physics, mechanics, etc. In this paper, we focus on constructing high-order algorithms for Riesz derivatives, where the convergence orders cover from the second order to the sixth order. Then we apply the established schemes to the Riesz type turbulent diffusion equation (or, Riesz space fractional turbulent diffusion equation). Numerical experiments are displayed which support the theoretical analysis.

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Authors and Affiliations

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

    Ding Hengfei

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

    Li Changpin

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

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Hengfei, D., Changpin, L. High-Order Algorithms for Riesz Derivative and their Applications (III). FCAA 19, 19–55 (2016). https://doi.org/10.1515/fca-2016-0003

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