Symmetric integrators based on continuous-stage Runge–Kutta–Nyström methods for reversible systems

摘要

In this paper, we study symmetric integrators for solving second-order ordinary differential equations on the basis of the notion of continuous-stage Runge–Kutta–Nyström methods. The construction of such methods heavily relies on the Legendre expansion technique in conjunction with the symmetric conditions and simplifying assumptions for order conditions. New families of symmetric integrators as illustrative examples are presented. For comparing the numerical behaviors of the presented methods, some numerical experiments are also reported.