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Global-in-Time \(H^1\)-Stability of L2-1\(_\sigma \) Method on General Nonuniform Meshes for Subdiffusion Equation

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Abstract

In this work the L2-1\(_\sigma \) method on general nonuniform meshes is studied for the subdiffusion equation. When the time step ratio is no less than 0.475329, a bilinear form associated with the L2-1\(_\sigma \) fractional-derivative operator is proved to be positive semidefinite and a new global-in-time \(H^1\)-stability of L2-1\(_\sigma \) schemes is then derived under simple assumptions on the initial condition and the source term. In addition, the sharp \(L^2\)-norm convergence is proved under the constraint that the time step ratio is no less than 0.475329.

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Funding

C. Quan is supported by NSFC Grant 12271241, Guangdong Basic and Applied Basic Research Foundation (No. 2023B1515020030), and Shenzhen Science and Technology Program (Grant No. RCYX20210609104358076).

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Authors and Affiliations

  1. SUSTech International Center for Mathematics, Southern University of Science and Technology, Shenzhen, China

    Chaoyu Quan

  2. Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China

    Xu Wu

  3. Department of Mathematics, Southern University of Science and Technology, Shenzhen, China

    Xu Wu

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  1. Chaoyu Quan
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  2. Xu Wu
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Correspondence to Xu Wu.

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Quan, C., Wu, X. Global-in-Time \(H^1\)-Stability of L2-1\(_\sigma \) Method on General Nonuniform Meshes for Subdiffusion Equation. J Sci Comput 95, 59 (2023). https://doi.org/10.1007/s10915-023-02184-8

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  • DOI: https://doi.org/10.1007/s10915-023-02184-8

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