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梯形公式局部外插法的稳定性

汤铭端   

  1. 北京永定计算站
  • 出版日期:1987-03-14 发布日期:1987-03-14

汤铭端. 梯形公式局部外插法的稳定性[J]. 计算数学, 1987, 9(3): 297-302.

STABILITY OF METHODS OF TRAPEZOIDAL RULE WITH LOCAL EXTRAPOLATION

  1. Tang Ming-duan Beijing Yongding Computer Genter
  • Online:1987-03-14 Published:1987-03-14
梯形公式外插法是求解刚性常微分方程初值问题 y′=f(t,y),y(a)=η,a≤t≤b(1)的一个比较有效的算法.它分为整体外插和局部外插.整体外插法仍保持A-稳定性,局部外插法则失去梯形公式的A-稳定性.但是梯形公式局部外插有相当大的稳定区域,而且精度一般比整体外插要好,所以它仍然是解刚性问题的一个有效方法.猜想偶数
The stability of the methods of trapezoidal rule with local extrapolation for the numericalintegration of ODEs is discussed. If the number of times of extrapolation is even, the methodsare A_0-stable and A(0)-stable. Similar methods of local extrapolation are also discussed andshown to be A_0-stable.
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[1] J. D. Lambert, Computational Methods in Ordinary Differential Equations, John Wily & Sons, 1973.
[2] W. H. Enright, F. E. Hull, B. Lindberg, Comparing numerical methods for stiff systems of ordinary differential equations. BIT. 15 (1975) . 10--48.
[3] 袁兆鼎、费景高,刘德贵,刚性常微分方程初值问题数值解法,待发表.
[4] 何爱芳,关于梯形法局部外插,计算数学,5:3(1983) ,326-331.
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