一类stiff稳定的线性多步法

A Class of Stiff-Stable Linear Multistep Methods

§1.引言 在常微分方程初值问题的数值方法中,线性多步法是最简单、使用最广泛的方法之一.但由于现存的线性多步方法的绝对稳定区域较小,以致在解刚性(Stiff)微分方程中受到很大限制.本文在BDF方法及[2]的基础上增加二个修正项,构造一类修正BDF的线性多步法,具有较大的绝对稳定区域.其结果如下:此类修正方法的阶与同步数的BDF方法的阶一致,其绝对稳定区域与低二阶的BDF方法大致相同,甚至更好,并给出了参数的取值范围.

In this paper, On the basis of the BDF, a class of stiff-stable linear multistep methodswith two paramaters α and β is given, which improves the numerical stability of the BDFs. Theregion of absolute stability of the new method of order k is almost the same as that of the BDFof order k-2.