Exponential Runge-Kutta methods for delay equations in the sun-star abstract framework
<|reference_start|>Exponential Runge-Kutta methods for delay equations in the sun-star abstract framework: Exponential Runge-Kutta methods for semilinear ordinary differential equations can be extended to abstract differential equations, defined on Banach spaces. Thanks to the sun-star theory, both delay differential equations and renewal equations can be recast as abstract differential equations, which motivates the present work. The result is a general approach that allows us to define the methods explicitly and analyze their convergence properties in a unifying way.<|reference_end|>
@article{ando'2024exponential,
    title={Exponential Runge-Kutta methods for delay equations in the sun-star
  abstract framework},
    author={Alessia Ando' and Rossana Vermiglio},
    journal={arXiv preprint arXiv:2410.00498},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.00498},
    primaryClass={math.NA cs.NA}
}