Abstract
In this paper we present a methodology to produce efficient multistep methods with constant coefficients for second order initial or boundary value problems with periodical and/or oscillating solutions. The methodology which we knew until now was the developed by Simos and co-workers (see [6]) and was based on the minimization of the phase-lag. With this methodology we couldn't know for the specific coefficients the order of the phase-lag derivatives. With the proposed methodology we can determine the free coefficients of a multistep method not only via the minimization of the phase-lag but via also the the minimization of the derivatives of the phase-lag. With this new methodology we can know at the end of analysis the order of phase-lag but also the order of the derivatives of the phase-lag.