Error analysis of a backward L2 method on graded meshes for linear and semilinear subdiffusion equations
Year: 2026
Type: preprint
Abstract: Time-fractional linear and semilinear parabolic equations with a Caputo time derivative of order $α\in(0,1)$ are considered. Their solutions exhibit an initial singularity of type $t^σ$ for any fixed $σ\in (0,1) \cup (1,2)$. A backward L2-type discrete fractional-derivative operator of order $3-α$ is considered on nonuniform temporal meshes. Sufficient conditions for inverse monotonicity of this operator areestablished. Hence, sharp pointwise-in-time error bounds are obtained on graded temporal meshes with arbitrary degree of grading. The theoretical findings are illustrated by numerical experiments.
Source: arXiv (Cornell University)
Authors: Kopteva, Natalia, Wang, Lu
Institutions: University of Limerick, Harbin Institute of Technology
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G8419660867
OpenAlex ID: W7222923534