Rational methods for abstract linear, non-homogeneous problems without order reduction
<|reference_start|>Rational methods for abstract linear, non-homogeneous problems without order reduction: Starting from an A-stable rational approximation to $\rm{e}^z$ of order $p$, $$r(z)= 1+ z+ \cdots + z^p/ p! + O(z^{p+1}),$$ families of stable methods are proposed to time discretize abstract IVP's of the type $u'(t) = A u(t) + f(t)$. These numerical procedures turn out to be of order $p$, thus overcoming the order reduction phenomenon, and only one evaluation of $f$ per step is required.<|reference_end|>
@article{arranz-simón2024rational,
    title={Rational methods for abstract linear, non-homogeneous problems without
  order reduction},
    author={Carlos Arranz-Sim'on, Cesar Palencia},
    journal={arXiv preprint arXiv:2405.04195},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.04195},
    primaryClass={math.NA cs.NA}
}