A SINGLY DIAGONALLY IMPLICIT RUNGE-KUTTA-NYSTR?M METHOD WITH DISPERSION OF HIGH ORDER

摘要

In this paper a singly diagonally implicit Runge-Kutta-Nystr?m (RKN) method is developed for second-order ordinary differential equations with periodical solutions. The method has algebraic order four and phase-lag order eight at a cost of four function evaluations per step. This new method is more accurate when compared with current methods of similar type for the numerical integration of second-order differential equations with periodic solutions, using constant step size.