A trigonometrically adapted 6(4) explicit Runge–Kutta–Nyström pair to solve oscillating systems

Abstract

In this study, a trigonometrically adapted 6(4) explicit Runge–Kutta–Nyström (RKN) pair with six stages is formulated, considering a previous method developed by El‐Mikkawy and Rahmo. The obtained adapted pair integrates exactly the usual test equation: . The local truncation error of the new method is presented, showing that the algebraic order of the original method is maintained. The periodicity interval of the new method is computed, showing that the developed method is “almost” P‐stable. The numerical examples considered clearly show the superiority of the new developed embedded pair over other RKN methods of algebraic orders 6(4) with six stages appeared in the literature.