Trigonometrically-fitted ARKN methods for perturbed oscillators

In this paper, new and robust trigonometrically-fitted adapted Runge–Kutta–Nyström methods for the numerical integration of perturbed oscillators are presented, which combine the features of trigonometrically-fitted methods with ARKN methods. Based on the linear-operator theory, the necessary and sufficient order conditions for these methods are derived. The numerical experiments are accompanied to show the efficiency and competence of our methods in comparison with some well-known methods.