We revisit the old problem of nding the stability and instability intervals of a secondorder elliptic equation on the real line with periodic coe cients (Hill’s equation). It is well known that the stability intervals correspond to the spectrum of the Bloch family of operators de ned on a single period. Here we propose a characterization of the instability intervals. We introduce a new family o...

In this manuscript, we propose a parametric family of iterative methods fourth-order convergence, and the stability class is studied through use tools complex dynamics. We obtain fixed critical points rational operator associated with family. A analysis allows us to find sets values parameter for which behavior corresponding method stable or unstable; therefore, can select regions in behave mor...