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

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 Grönwall inequality and a rigorous analysis for the truncation errors. Numerical experiments are provided to demonstrate the effectiveness of our theoretical analysis.

arXiv comment19 pages

References in corpus (4)

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• Time-stepping error bounds for fractional diffusion problems with non-smooth initial data