On modified TDRKN methods for second-order systems of differential equations.

This paper concerns modified Two-Derivative Runge–Kutta–Nyström (TDRKN) methods for solving second-order initial value problems. Compromised with the deduced order and symmetry criteria, two implicit and forth-order two-stage TDRKN schemes are derived through a mixed collocation approach. Phase and periodic stability features are examined. Numerical experiments are carried out to illustrate the effectiveness and competence of our new methods. Comparisons with existing highly accurate and efficient numerical methods are given. [ABSTRACT FROM AUTHOR]