中文摘要：

研究一类二阶延迟微分方程Runge-Kutta-Nystroem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。

英文摘要：

The stability of Runge-Kutta-Nystroem methods is studied for a class of second order delay differential equations. 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.