多导块方法的稳定性分析  

The Numerical Stabilities of Multiderivative Block Method

作　　者：匡蛟勋[1] 林玉华[1] 

机构地区：[1]上海师范大学数学系

出　　处：《应用数学和力学》1993年第2期119-126,共8页Applied Mathematics and Mechanics

摘　　要：文[1]中提出了一种使用高阶导数的块隐式单步法,并在文末留下一个问题:即对给定的方法中使用的最高阶导数阶数l≥1,为使该方法是A—稳定的,块的大小k应满足什么条件?本文将彻底地解答这个问题.首先,我们给出稳定函数ξ_k(?)=P(?)/Q(?)中多项式P( )及Q(?)的系数的显式表达式,并证明P(-?)=Q(?);另外,我们使用计算机符号运算及对角Pade＇逼近公式,对任意的l≥1,给出了为使方法A—稳定时块的大小k应满足的条件.In [ 1 ], a class of uiultiderivative block methods (MDBM) -was studied for the mumerical solutions of stiff ordinary differential equations. This paper is aimed at solving the problem proposed in [1] that what conditions should be fulfilled for MDBMs in order to guarantee the A-stabilities. The explicit expressions of the polynomials P( h) and Q(7t) in the stability functions k,(h) = P(h) IQ(h) are given. Furthermore, we prove P( - h) = Q(h), With the aid of symbolic computations and the expressions of diagonal Fade' approximations, we obtained the biggest block size k of the -4-stable MDBM for any given I (the order of the highest derivatives used in MDBM, 1>1).

关 键 词：稳定性 多导块法 块稳式单步法 

分 类 号：O241.8[理学—计算数学]