Numerical solution of constant coefficient linear delay differential equations as abstract Cauchy problems

In this paper we present an approach, for the numerical solution of linear delay differential equations, different from the classical step-by-step method. We restate the equation as an abstract Cauchy problem and then we discretize it in a system of ordinary differential equations. The scheme of discretization is proved to be convergent. Moreover the asymptotic stability is investigated for two significan classes of asymptotically stable problems.