中文摘要：

本文给出了一类比Adams—Bashforth方法的局部截断误差主项系数小和绝对稳定区间大的显式k阶线性k步法基本公式．作者求出了公式的分数形式的精确系数，阶数和局部截断误差主项系数，给出了3-9步公式的绝对稳定区间，构造了由新公式的4阶显式公式和一个同阶隐式基本公式组合而成的特殊预估一校正方法，它的绝对稳定区间大于预估公式而且等于校正公式，比著名的Adams—Bashforth—Moulton预估校正方法的绝对稳定区间大，最后用数值试验对结果进行了验证，适合于求解常微分方程初值问题．

英文摘要：

In this paper, a new class basic formulas of linear k step explicit methods of k order, the stability better than Adams-Bashforth methods, is given. The fractal coefficients of the formulas of 3-step to 9 in this class are deduced, the orders and error coefficients axe 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 famous Adams-Bashforth-Moulton predictor- corrector method. Finally, by means of the numerical experiment, it is verified that are stable and suitable for solving initial value problems of ordinary differential equations.