Abstract
A new family of modified two-derivative Runge-Kutta-Nyström (TDRKN) methods are proposed for solving initial value problems of second-order oscillatory ordinary differential equations. Order conditions are obtained via the Nyström tree theory and the B-series theory. Trigonometric fitting conditions are derived. Two practical explicit trigonometrically fitted TDRKN (TFTDRKN) methods are constructed. The phase properties of the new integrators are examined and their periodicity regions are obtained. The results of numerical experiments show the efficiency and competence of the new methods compared with some highly efficient codes in the literature.
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