@Article{JCM-42-3,
author = {Li, Dongfang and Qin, Hongyu and Zhang, Jiwei},
title = {Sharp Pointwise-in-Time Error Estimate of L1 Scheme for Nonlinear Subdiffusion Equations},
journal = {Journal of Computational Mathematics},
year = {2024},
volume = {42},
number = {3},
pages = {662--678},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2205-m2021-0316},
url = {https://global-sci.com/article/91073/sharp-pointwise-in-time-error-estimate-of-l1-scheme-for-nonlinear-subdiffusion-equations}
}