Moreta Santos, María Jesús2023-06-162023-06-162021-09-102227-739010.3390/math9182225https://hdl.handle.net/20.500.14352/5016In this work, we develop a new class of methods which have been created in order to numerically solve non-linear second-order in time problems in an efficient way. These methods are of the Rosenbrock type, and they can be seen as a generalization of these methods when they are applied to second-order in time problems which have been previously transformed into first-order in time problems. As they also follow the ideas of Runge–Kutta–Nyström methods when solving second-order in time problems, we have called them Rosenbrock–Nyström methods. When solving non-linear problems, Rosenbrock–Nyström methods present less computational cost than implicit Runge–Kutta–Nyström ones, as the non-linear systems which arise at every intermediate stage when Runge–Kutta–Nyström methods are used are replaced with sequences of linear ones.engjournal articlehttps://doi.org/10.3390/math9182225open accessSecond-order in time problemsNon-linear problemsRosenbrock type methods.Análisis Numérico1206: Análisis Numérico