中文摘要：

推导了一个3阶的隐式线性3步法公式，它的绝对稳定区间达到（-9．3333，0），可用于常微分方程初值问题的求解，且具有较好的稳定性。公式的相容性和收敛性在文章中得到验证，并描绘出稳定区域。最后用数值试验证明了此公式对中等刚性问题的有效性。

英文摘要：

This paper deals with the derivation of a implicit linear 3 - step formula of 3 - order in which its absolutely stable interval could reach （ -9. 3333,0）. It can be used to solve initial value problems of ordinary differential equation and has better stability. In this article, we deduce the formula and prove its consistency and convergence. At the same time, we draw the abso- lutely stable region and verify its validity for some questions of moderately stiff equations by numerical experiment.