显式线性三步二阶方法的稳定性讨论  

A DISCUSSION OF THE STABILITY ON EXPLICIT LINEAR 3-STEP METHODS OF ORDER 2

作　　者：李林忠[1] 何轶良[1] 陈小飞 

机构地区：[1]哈尔滨工业大学

出　　处：《高等学校计算数学学报》1994年第1期42-53,共12页Numerical Mathematics A Journal of Chinese Universities

摘　　要：1 引 言 关于常微分方程初值问题 y′=f(t,y), t∈[t_0,T]R, y(t_0)=y_0, y,f∈R^m,m≥1, (1.1)存在许多数值方法,显式线性多步法,特别是Adams—Bashforth方法。In this paper, the stability of explicit linear 3-step methods of order 2 is discussed. The optimal methods based on the longest stability interval, the largest area of stability regions and the maximum height of stability regions along the imaginary axis are determined. The stability regions of the methods can be far larger than known explicit linear multistep methods'. Practical calculations have shown that they are adaptive for solving the medium sized stiff problems.

关 键 词：常微分方程 线性多步法 稳定性 

分 类 号：O241.81[理学—计算数学]