Error analysis of an L2-type method on graded meshes for semilinear subdiffusion equations
<|reference_start|>Error analysis of an L2-type method on graded meshes for semilinear subdiffusion equations: 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.<|reference_end|>
@article{kopteva2024error,
    title={Error analysis of an L2-type method on graded meshes for semilinear
  subdiffusion equations},
    author={Natalia Kopteva},
    journal={arXiv preprint arXiv:2408.03420},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.03420},
    primaryClass={math.NA cs.NA}
}