New fractional step Runge–Kutta–Nyström methods up to order three

Abstract

Fractional 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.