中文摘要：

本文研究了分段连续型微分方程x1（t）=ax（t）＋bx（3[（t＋1）/3]）Euler-Maclaurin方法的数值稳定性问题.利用特征分析的方法,获得了数值解稳定的充分条件,进而证明了Euler-Maclaurin方法保持了精确解的稳定性.最后给出了一些数值例子.

英文摘要：

In this paper,we investigate the numerical stability of Euler-Maclaurin method for differential equation with piecewise constant arguments x1（t）=ax（t）＋bx（3[（t＋1）/3]）.By the method of characteristic analysis,the sufficient conditions of stability for the numerical solution are obtained.Moreover,we show that the Euler-Maclaurin method preserves the stability of the exact solution.Finally,some numerical examples are given.