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Pointwise-in-time error bounds for semilinear and quasilinear fractional subdiffusion equations on graded meshes

Published: June 15, 2025 | arXiv ID: 2506.12954v1

By: Natalia Kopteva, Sean Kelly

Potential Business Impact:

Solves tricky math problems faster.

Business Areas:
Quantum Computing Science and Engineering

Time-fractional semilinear and quasilinear parabolic equations with a Caputo time derivative of order $\alpha\in(0,1)$ are considered, solutions of which exhibit a singular behaviour at an initial time of type $t^\sigma$ for any fixed $\sigma \in (0,1) \cup (1,2)$. The L1 scheme in time is combined with a general class of discretizations for the semilinear term. For such discretizations, we obtain sharp pointwise-in-time error bounds on graded temporal meshes with arbitrary degree of grading. Both semi-discretizations in time and full discretizations using finite differences and finite elements in space are addressed. The theoretcal findings are illustrated by numerical experiments.

Country of Origin
🇮🇪 Ireland

Page Count
21 pages

Category
Mathematics:
Numerical Analysis (Math)