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.

翻译：从$\rm{e}^z$的$p$阶A-稳定有理逼近出发，$$r(z)= 1+ z+ \cdots + z^p/ p! + O(z^{p+1}),$$提出了适用于$u'(t) = A u(t) + f(t)$型抽象初值问题时间离散化的稳定方法族。这些数值方法具有$p$阶精度，从而克服了阶降现象，且每步仅需一次$f$的求值。