Extended explicit Pseudo two-step Runge-Kutta-Nyström methods for general second-order oscillatory systems

Abstract

Explicit pseudo two-step extended Runge-Kutta-Nyström (EPTSERKN) methods for the numerical integration of general second-order oscillatory differential systems are discussed in this paper. New explicit pseudo two-step Runge-Kutta-Nyström (EPTSRKN) methods and explicit extended Runge-Kutta-Nyström (ERKN) methods are derived. We give the global error analysis of the new methods. The s-stages new methods are of order \(s+1\) with some suitable nodes. Numerical experiments are carried out to show the efficiency and robustness of the new methods.