Error analysis of an L2-type method on graded meshes for semilinear subdiffusion equations
Abstract
A semilinear initial-boundary value problem with a Caputo time derivative of fractional order $\alpha\in(0,1)$ is considered, solutions of which typically exhibit a singular behaviour at an initial time. For an L2-type discretization of order $3-\alpha$, we give sharp pointwise-in-time error bounds on graded temporal meshes with arbitrary degree of grading.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.03420
- arXiv:
- arXiv:2408.03420
- Bibcode:
- 2024arXiv240803420K
- Keywords:
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- Mathematics - Numerical Analysis