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A numerical approximation method for solving a three-dimensional space Galilei invariant fractional advection-diffusion equation

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Abstract

In this paper, a numerical approximation method for solving a three-dimensional space Galilei invariant fractional advection diffusion equation is presented. The convergence and stability of the numerical approximation method are discussed by a new technique of Fourier analysis. The solvability of the numerical approximation method also is analyzed. Finally, applying Richardson extrapolation technique, a high-accuracy algorithm is structured and the numerical example demonstrated the theoretical results.

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Authors and Affiliations

  1. School of Mathematical Science, Xiamen University, Xiamen, 361005, China

    Chang-Ming Chen

  2. School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Queensland, 4001, Australia

    F. Liu

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  1. Chang-Ming Chen
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  2. F. Liu
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Correspondence to F. Liu.

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Chen, CM., Liu, F. A numerical approximation method for solving a three-dimensional space Galilei invariant fractional advection-diffusion equation. J. Appl. Math. Comput. 30, 219–236 (2009). https://doi.org/10.1007/s12190-008-0168-7

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  • DOI: https://doi.org/10.1007/s12190-008-0168-7

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