中文摘要：

考虑一类k步k＋1阶线性多步法∑^kj=1αjyi＋j=h（βk-1fi＋k-1＋βkfi＋k）,αk=1,βk≠0,通过改进这类k步k＋1阶公式可以得到一类更稳定的k阶线性k步法隐式公式,使原来稳定区域比较小,甚至没有稳定区域和不收敛的公式,都变为A（α）稳定.并用数值实验证明了这类公式对刚性方程问题的有效性.

英文摘要：

We consider one class of k-step Linear Multi-step Method formulas of order k＋1,∑^kj=1αjyi＋j=h（βk-1fi＋k-1＋βkfi＋k）,αk=1,βk≠0,obtain one class of more stable implicit linear k -step formulas ofk -order through improving such class of k -step formulas of order k ＋ 1, and make the original small regional of stability, not even regional of stability and convergence formula into A（α） stable. Besides this we verify the validity for stiff equations by numerical experiment.