Year: 2024
Author: Dongfang Li, Hongyu Qin, Jiwei Zhang
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 3 : pp. 662–678
Abstract
An essential feature of the subdiffusion equations with the $α$-order time fractional derivative is the weak singularity at the initial time. The weak regularity of the solution is usually characterized by a regularity parameter $σ ∈ (0, 1) ∪ (1, 2).$ Under this general regularity assumption, we present a rigorous analysis for the truncation errors and develop a new tool to obtain the stability results, i.e., a refined discrete fractional-type Grönwall inequality (DFGI). After that, we obtain the pointwise-in-time error estimate of the widely used L1 scheme for nonlinear subdiffusion equations. The present results fill the gap on some interesting convergence results of L1 scheme on $σ ∈ (0, α) ∪ (α, 1) ∪ (1, 2].$ Numerical experiments are provided to demonstrate the effectiveness of our theoretical analysis.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2205-m2021-0316
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 3 : pp. 662–678
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Sharp pointwise-in-time error estimate L1 scheme Nonlinear subdiffusion equations Non-smooth solutions.