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刚性方程数值方法的危险性问题
引用本文:韩天敏,崔可发.刚性方程数值方法的危险性问题[J].计算数学,1979,1(4):331-335.
作者姓名:韩天敏  崔可发
作者单位:中国科学院计算中心 (韩天敏),中国科学院计算中心(崔可发)
摘    要:为了找出有效地处理Stiff方程的数值方法,Gear给出了数值方法Stiff稳定性的定义,见1]。根据这个定义,可以找出一些好的数值方法,例如基于数值微分的Gear方法,Enright的一阶导数方法等.但2]中通过两个具体的例子说明此类方法具有“危险


THE DANGEROUS PROPERTY OF NUMERICAL METHODS OF STIFF DIFFERENTIAL EQUATIONS
Institution:Han Tian-min;Cui Ke-fa Computing Center, Chinese Academy of Sciences
Abstract:A numerical method of stiff equations has "dangerous property" if it can notdiscover the instability of the system. The reason why the general methods make thisdangerous property is analysed in this paper. We also point out that the methodproposed in 4] does not have this dangerous property. B. Lindberg has showed astwo examples in 2]. He could not get the correct solution with the general methods(e.g. Gear's). However by the same examples the method in 4] detected the ap-pearance of eigenvalue with positive real immediately in the computing procedure.
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