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Mathematics > Numerical Analysis

arXiv:2208.01384 (math)
[Submitted on 2 Aug 2022 (v1), last revised 14 Sep 2022 (this version, v3)]

Title:Global-in-time $H^1$-stability of L2-1$_σ$ method on general nonuniform meshes for subdiffusion equation

Authors:Chaoyu Quan, Xu Wu
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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 $0.475329$.
Comments: arXiv admin note: text overlap with arXiv:2205.06060
Subjects: Numerical Analysis (math.NA)
MSC classes: 35R11, 65M12
Cite as: arXiv:2208.01384 [math.NA]
  (or arXiv:2208.01384v3 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2208.01384

Submission history

From: Chaoyu Quan [view email]
[v1] Tue, 2 Aug 2022 11:57:00 UTC (534 KB)
[v2] Mon, 12 Sep 2022 06:22:56 UTC (553 KB)
[v3] Wed, 14 Sep 2022 07:02:22 UTC (260 KB)
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