(untitled) (Journal of Computational Mathematics, 1993)
Characterizations of symmetric and symplectic Runge-Kutta methods, which are based on the W-transformation of Hairer and Wanner, are presented. Using these characterizations we construct two classes of high order symplectic (symmetric and algebraically stable or algebraically stable) Runge-Kutta methods. They include and extend known classes of high order implicit Runge-Kutta methods.