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High‐Order Algorithms for Riesz Derivative and Their Applications (I)

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  • Hengfei Ding
  • Changpin Li
  • YangQuan Chen

Abstract

We firstly develop the high‐order numerical algorithms for the left and right Riemann‐Liouville derivatives. Using these derived schemes, we can get high‐order algorithms for the Riesz fractional derivative. Based on the approximate algorithm, we construct the numerical scheme for the space Riesz fractional diffusion equation, where a fourth‐order scheme is proposed for the spacial Riesz derivative, and where a compact difference scheme is applied to approximating the first‐order time derivative. It is shown that the difference scheme is unconditionally stable and convergent. Finally, numerical examples are provided which are in line with the theoretical analysis.

Suggested Citation

  • Hengfei Ding & Changpin Li & YangQuan Chen, 2014. "High‐Order Algorithms for Riesz Derivative and Their Applications (I)," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:653797
    DOI: 10.1155/2014/653797
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    References listed on IDEAS

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    1. Manuel Duarte Ortigueira, 2006. "Riesz potential operators and inverses via fractional centred derivatives," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2006, pages 1-12, August.
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