On using explicit Runge–Kutta–Nyström methods for the treatment of retarded differential equations with periodic solutions

摘要

In this work we dial with the treatment of second order retarded differential equations with periodic solutions by explicit Runge–Kutta–Nyström methods. In the past such methods have not been studied for this class of problems. We refer to the underline theory and study the behavior of various methods proposed in the literature when coupled with Hermite interpolants. Among them we consider methods having the characteristic of phase–lag order. Then we consider continuous extensions of the methods to treat the retarded part of the problem. Finally we construct scaled extensions and high order interpolants for RKN pairs which have better characteristics compared to analogous methods proposed in the literature. In all cases numerical tests and comparisons are done over various test problems.