A family of high-order accurate contour integral methods for strongly continuous semigroups
<|reference_start|>A family of high-order accurate contour integral methods for strongly continuous semigroups: Exponential integrators based on contour integral representations lead to powerful numerical solvers for a variety of ODEs, PDEs, and other time-evolution equations. They are embarrassingly parallelizable and lead to global-in-time approximations that can be efficiently evaluated anywhere within a finite time horizon. In this article, we propose a family of new high-order quadrature schemes for strongly continuous semigroups based on regularized contour integral representations. Our algorithms are accompanied by explicit high-order error bounds and near-optimal parameter selection. We demonstrate key features of the schemes on singular first-order PDEs from Koopman operator theory.<|reference_end|>
@article{horning2024a,
    title={A family of high-order accurate contour integral methods for strongly
  continuous semigroups},
    author={Andrew Horning and Adam R. Gerlach},
    journal={arXiv preprint arXiv:2408.07691},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.07691},
    primaryClass={math.NA cs.NA}
}