Bujanda, BlancaMoreta Santos, María JesúsJorge, Juan Carlos2024-12-102024-12-102019B. Bujanda, M. Moreta y J. C. Jorge. New fractional Runge-Kutta-Nyström methods up to order three, Applied Mathematics and Computation, Vol. 366 (2020). Article 124743, 1 – 19.0096-300310.1016/j.amc.2019.124743https://hdl.handle.net/20.500.14352/112330Fractional Step Runge–Kutta–Nyström (FSRKN) methods have been revealed to be an excel- lent 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 clas- sical 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 sat- isfy 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.engjournal article1873-5649https://doi.org/10.1016/j.amc.2019.124743https://www.sciencedirect.com/science/article/pii/S0096300319307350restricted access519.6Fractional Step Runge–Kutta–Nyström methodsSecond-order partial differential equationsCienciasEcuaciones diferencialesMatemáticas (Matemáticas)Análisis numérico1206.13 Ecuaciones Diferenciales en Derivadas Parciales1206.01 Construcción de Algoritmos