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Numerical Analysis of the Nonuniform Fast L1 Formula for Nonlinear Time–Space Fractional Parabolic Equations

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Abstract

Basing on the nonuniform fast L1 formula, an efficient numerical scheme is proposed for nonlinear time–space fractional parabolic equations. The stability and convergence of the numerical scheme are rigorously established. The discrete energy dissipation property of the numerical scheme based on graded temporal mesh is given. Finally, several numerical experiments are provided to verify the theoretical results.

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Data Availability

The datasets generated during the current study are available from the corresponding author on reasonable request.

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Funding

This work is supported by the Scientific Research Fund of Hunan Provincial Education Department of China under Grant (NO.21B0685) and Science and technology planning project of Shaoyang science and Technology Bureau (NO.2020GZ88).

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Authors and Affiliations

  1. Department of Mathematics, Shaoyang University, Shaoyang, Hunan, 422000, People’s Republic of China

    Zhiyong Xing

  2. Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, Hunan, 411105, People’s Republic of China

    Liping Wen

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  1. Zhiyong Xing
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Both authors contributed equally to writing of this paper. Both authors read and approved the final manuscript.

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Correspondence to Zhiyong Xing.

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Xing, Z., Wen, L. Numerical Analysis of the Nonuniform Fast L1 Formula for Nonlinear Time–Space Fractional Parabolic Equations. J Sci Comput 95, 58 (2023). https://doi.org/10.1007/s10915-023-02186-6

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  • DOI: https://doi.org/10.1007/s10915-023-02186-6

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