显式线性多步法的最优稳定区域  

ABSOLUTELY STABLE OPTIMUM REGION FOR THE EXPLICIT LINEAR MULTISTEP METHODS

作　　者：李雨[1] 魏玉芬[1] 么焕民[2] 

机构地区：[1]黑龙江八一农垦大学 [2]哈尔滨师范大学

出　　处：《哈尔滨师范大学自然科学学报》2009年第4期28-31,共4页Natural Science Journal of Harbin Normal University

摘　　要：从线性多步法稳定区域所包含的负实轴的长度α,稳定区域的面积S以及稳定区域在虚轴方向上所达到的最大高度Ih三个方面,讨论了四步法的最优稳定性.在误差常数变化不大的情况下,对于特定的方法类找到了具有"最优"稳定区域的方法,求出了显式线性四步法的最优稳定区域和取得最优稳定区域的条件.This paper deal with the absolutely stable region for the explicit linear muhistep methods. Ameliorate the stability of the linear muhistep methods in three aspects including the maximal positive real axis length , the maximal acreage S and the maximal height Ih of imaginary axis of the region of absolutely stable. This paper found the methods which have the optimum stable character with the error constants are not much larger, and work out the optimum region of the explicit linear 4 step methods.

关 键 词：线性多步法 绝对稳定区域 增大稳定区间 

分 类 号：O241.81[理学—计算数学] O175.13[理学—数学]