The stability of rational approximations of cosine functions on Hilbert spaces

In this paper, it is proved the stability of rational methods for the time discretization of abstract well-posed second order in time problems where the differential operator generates a cosine function. The particular case of operators associated to a sesquilinear form is studied in detail. These rational methods are suitable for these problems and they can be defined, for example, by using Runge–Kutta–Nyström methods.