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解Stiff常微分方程组初值问题的线性隐式方法

孙耿   

  1. 中国科学院数学研究所
  • 出版日期:1983-04-14 发布日期:1983-04-14

孙耿. 解Stiff常微分方程组初值问题的线性隐式方法[J]. 计算数学, 1983, 5(4): 344-352.

LINEARLY IMPLICIT METHODS FOR STIFF SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS

  1. Sun Geng Institute of Mathematics, Academia Sinica
  • Online:1983-04-14 Published:1983-04-14
对于Stiff常微分方程组初值问题的数值解,人们为了保证数值解过程误差传播的有界性,经常使用的方法之一是隐式的线性多步法.而在解由隐式线性多步法所产生的非线性方程组时,总是采用Newton-Raphson迭代方法.为此就要给出适当的预估式和计算
In this paper, starting with the multistep methods and one-leg methods with variablecoefficients, we construct two classes of linearly implicit methods. For the linear autonomo-us system y'= Ay, these linearly implicit methods respectively are identical with certain im-plicit multistep and one-leg methods. Moreover, the first (2 k-p)terms of the local trunca-tion error in the linearly implicit and implicit one-leg methods are the same.
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[1] 孙耿,毛祖范,两类线性隐式方法,计算数学,3:2(1981) ,169-174.
[2] G. Dahlquist, Some propertes of linear multistep and One-leg methods for ODEs, Report TRITANA-7904, 1979.
[3] ----,Some contractivity questions for one-log-and linear multistep methods, Report TRITA-NA-7905, 1979.
[4] O. Nevanlinna, W. Liniger, Contractive methods for stiff DEs, Part I, BIT 18, 1978, 457-474.
[5] O. Nevanlinna, W. Liniger, Contractive methods for stiff DEs, Part I, BIT 18, 1979. 457-474.
[6] 孙耿,毛祖范,关于变更的Adams-Moulton方法,计算数学,5:2(1983) ,113-118.
[7] G.Dahlquist,来华讲学的讲稿,LS-15,1979.
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