中文摘要：

本文讨论了向前型分段连续微分方程Euler-Maclaurin方法的收敛性和稳定性,给出了Euler-Maclaurin方法的稳定条件,证明了方法的收敛阶是2n＋2,并且得到了数值解稳定区域包含解析解稳定区域的条件,最后给出了一些数值例子用以验证本文结论的正确性.

英文摘要：

This paper is concerned with the convergence and the stability of Euler-Maclaurin methods for solutions of differential equations with piecewise constant arguments of advanced type.The conditions of stability for the Euler-Maclaurin methods are given.It is proved that the order of convergence is 2n＋2.And the conditions under which the numerical stability region contains the analytic stability region are obtained.Finally,several numerical examples are given to demonstrate our main results.