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High order finite difference method for time-space fractional differential equations with Caputo and Riemann-Liouville derivatives

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Abstract

We consider high order finite difference methods for two-dimensional fractional differential equations with temporal Caputo and spatial Riemann-Liouville derivatives in this paper. We propose a scheme and show that it converges with second order in time and fourth order in space. The accuracy of our proposed method can be improved by Richardson extrapolation. Approximate solution is obtained by the generalized minimal residual (GMRES) method. A preconditioner is proposed to improve the efficiency for the implementation of the GMRES method.

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Authors and Affiliations

  1. Department of Mathematics, University of Macau, Macau, China

    Seakweng Vong, Pin Lyu, Xu Chen & Siu-Long Lei

Authors
  1. Seakweng Vong
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  2. Pin Lyu
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  3. Xu Chen
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  4. Siu-Long Lei
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Corresponding author

Correspondence to Seakweng Vong.

Additional information

The first author is supported by the grant MYRG2015-00064-FST from University of Macau and Macao Science and Technology Development Fund (FDCT) 001/2013/A. The fourth author is supported by Macao Science and Technology Development Fund (FDCT) 115/2013/A3.

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Vong, S., Lyu, P., Chen, X. et al. High order finite difference method for time-space fractional differential equations with Caputo and Riemann-Liouville derivatives. Numer Algor 72, 195–210 (2016). https://doi.org/10.1007/s11075-015-0041-3

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  • DOI: https://doi.org/10.1007/s11075-015-0041-3

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