PreprintarXiv licencearXiv
Error analysis of a backward L2 method on graded meshes for linear and semilinear subdiffusion equations
Abstract
Time-fractional linear and semilinear parabolic equations with a Caputo time derivative of order α∈(0,1) are considered. Their solutions exhibit an initial singularity of type tσ for any fixed σ∈ (0,1) ∪ (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.
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BibTeX
@misc{kopteva2026error,
title = {{Error analysis of a backward L2 method on graded meshes for linear and semilinear subdiffusion equations}},
author = {Natalia Kopteva and Lu Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23780},
eprint = {2610.23780},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23780},
}
RIS
TY - UNPB
TI - Error analysis of a backward L2 method on graded meshes for linear and semilinear subdiffusion equations
AU - Natalia Kopteva
AU - Lu Wang
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23780
UR - https://arxiv.org/abs/2610.23780
AB - Time-fractional linear and semilinear parabolic equations with a Caputo time derivative of order α∈(0,1) are considered. Their solutions exhibit an initial singularity of type t^σ for any fixed σ∈ (0,1) ∪ (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.
ER -