一类k步k+2阶的二阶导数方法

A class of stiffly stable k-step second derivative methods of order k+2

Enright方法是一类k步k+2阶的二阶导数线性多步法,其中1-7步法公式都具有刚性稳定性,适用于刚性方程组求解.寻找到一类非Enright类型的可用于刚性方程组求解的k步k+2阶的二阶导数线性多步法,其中1-8步法公式都具有刚性稳定性且稳定区域比同阶的Enright方法大.数值实验证明了这类公式对刚性方程问题有效.

Enright methods are a class of k be stiffly stable for k = 1 -7 and which show to - step second derivative methods of order k ＋ 2, which turn out to be suitable for stiff system of ordinary differential equations. This paper presents a class of k - step second derivative methods of order k ＋ 2 which are suitable for stiff system of ordinary differential equations. These formulas turn out to be stiffly stable for k = 1 - 8 and have a larger absolute stability region than that of Enright methods. The validity for stiff equations by numerical experiment is verified.