A TRIGONOMETRICALLY ADAPTED EMBEDDED PAIR OF EXPLICIT RUNGE-KUTTA-NYSTR¨OM METHODS TO SOLVE PERIODIC SYSTEMS

Abstract

In this paper a 5(3) pair of explicit trigonometrically adapted Runge-Kutta-Nystr¨om methods with four stages is derived based on an explicit pair appeared in the literature. The new adapted method is able to integrate exactly the usual test equation: y′′ = −w²y. The local truncation error of the new method is obtained, proving that the algebraic order of convergence is maintained. The stability interval of the new method is obtained, showing that the proposed method is absolutely stable. The numerical experiments performed demonstrate the robustness of the new embedded pair in comparison with some standard codes available in the literature.