Bujanda Cirauqui, BlancaMoreta, M. JesúsJorge Ulecia, Juan Carlos2020-03-232022-02-0120200096-300310.1016/j.amc.2019.124743https://academica-e.unavarra.es/handle/2454/36564Fractional Step Runge–Kutta–Nyströ (FSRKN) methods have been revealed to be an excellent option to integrate numerically many multidimensional evolution models governed by second order in time partial differential equations. These methods, combined with suitable spatial discretizations, lead to strong computational cost reductions respect to many classical implicit time integrators. In this paper, we present the construction process of several implicit FSRKN methods of two and three levels which attain orders up to three and satisfy adequate stability properties. We have also performed some numerical experiments in order to show the unconditionally convergent behavior of these schemes as well as their computational advantages.26 p.application/pdfeng© 2019 Elsevier Inc. This manuscript version is made available under the CC-BY-NC-ND 4.0.Fractional Step Runge-Kutta-Nyströ methodsSecond-order partial differential equationsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess