一类二阶延迟微分方程的Runge-Kutta-Nystr(o)m方法的稳定性

摘要

研究一类二阶延迟微分方程Runge-Kutta-Nystr(o)m方法的稳定性.用该方法直接离散二阶延迟微分方程,给出该方法稳定的一个充要条件,并在此基础上给出一个简化的稳定性判别条件.%The stability of Runge-Kutta-Nystrom methods is studied for a class of second order delay differential e-quations. This method is to directly discretize the second order delay differential equations. A sufficient and necessary condition under which the numerical solutions preserve the stability are obtained, and on this basis a simplified criterion of the stability is given.