  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.
