A 5(3) pair of explicit Runge–Kutta–Nyström methods for oscillatory problems

New Runge–Kutta–Nyström methods especially designed for the numerical integration of periodic initial value problems are presented in this paper. They are able to integrate exactly the harmonic oscillator. Here we analyze the construction of an embedded 5(3) RKN pair with four stages. Numerical experiments indicate that the new pair is more efficient than some previously derived RKN pairs.