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arXiv · 2101.04554

Sharp pointwise-in-time error estimate of L1 scheme for nonlinear subdiffusion equations

Dongfang Li·Hongyu Qin·Jiwei Zhang
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Abstract

An essential feature of the subdiffusion equations with the $\alpha$-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 $\sigma\in (0,1)\cup(1,2)$. Under this general regularity assumption, we here obtain the pointwise-in-time error estimate of the widely used L1 scheme for nonlinear subdiffusion equations. To the end, we present a refined discrete fractional-type Gr\"onwall inequality and a rigorous analysis for the truncation errors. Numerical experiments are provided to demonstrate the effectiveness of our theoretical analysis.

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Dongfang Li, Hongyu Qin, Jiwei Zhang. 2021-01-12. Sharp pointwise-in-time error estimate of L1 scheme for nonlinear subdiffusion equations. https://arxiv.org/abs/2101.04554

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