一类含有稳定参数的Gear型隐式方式

A Class of Gear Implict Methods with Stable Parameter

本文导出解ｓｔｉｆｆ方程的一类含有稳定参数Ｓ的Ｋ步Ｋ阶的ｓｔｉｆｆ稳定的Ｇｅａｒ型隐式方法，我们可以通过适当选取参数Ｓ，改进其绝对稳定性。保证零稳定和无穷远稳定．它比相应的Ｇｅａｒ方法［１］。变更的Ｇｅａｒ方法［３］和Ｅｎｒｉｇｈｔ方法［２］有更大的绝对稳定域，并且构造方便，计算简单。

A class of Gear implicit methods with stable parameter S that are of K order stiffly stable K step methods has been derived for the solutiou of stiff equations. The parameter S can be appropriately chosen so as to improve abso - lute stability and to assure- zero-stability as well as infinite stability. Its sta - bility regions are latger than corresponding Gear's method, modified Gear's me- thod and-Enright's method, and with much constructing convenience and compu - ting simplicity.