中文摘要：

本文首先给出了一类比Adams—Moulton方法的绝对稳定区间大的隐式k＋1阶线性k步法基本公式．求出了3-9步新公式的分数形式的精确系数，阶数，局部截断误差主项系数和绝对稳定区间，然后构造了由4阶隐式新公式和同阶显式NystrSm公式组合而成的预估-校正方法，比著名的Adams—Bashforth—Moulton和Nystr6m—Adams—Moulton预估校正方法的绝对稳定区间大，最后用对比数值试验对结果进行了验证．

英文摘要：

In this paper, a new class basic formulas of linear k step implicit methods of k ＋ 1 order, the stability better than Adams-Moulton methods, is given. The fractal coefficients of the formulas of 3-step to 9 in this class are deduced, the orders and error coefficients are also gotten. We computed their absolute stability interval. It is that the absolute stability interval of predictor-corrector method composed of a new 4 order explicit formula and a new 4 order implicit basic formula large than well-known Adams-Bashforth-Moulton and Nystrom- Adams-Moulton predictor-corrector method.Finally, by means of the numerical experiment, it is verified that are stable.