## 留言板

 引用本文: 杨逢建, 张爱国, 陈新明. 怎样利用函数exp(q)的含参有理逼近构造高阶指数拟合方法[J]. 应用数学和力学, 1999, 20(9): 955-960.
Yang Fengjian, Zhang Aiguo, Chen Xinming. On Construction of High Order Exponentially Fitted Methods Based on Parameterized Rational Approximations to exp(q)[J]. Applied Mathematics and Mechanics, 1999, 20(9): 955-960.
 Citation: Yang Fengjian, Zhang Aiguo, Chen Xinming. On Construction of High Order Exponentially Fitted Methods Based on Parameterized Rational Approximations to exp(q)[J]. Applied Mathematics and Mechanics, 1999, 20(9): 955-960.

• 中图分类号: O24

## On Construction of High Order Exponentially Fitted Methods Based on Parameterized Rational Approximations to exp(q)

• 摘要: 得到了指数函数exp(q)的含双参数α、β的(4,4)有理逼近的表达式及其为A-可接受的充要条件,由此构造了精确阶可达6至8阶的四阶导数单步指数拟合方法与三阶导数混合单步指数拟合方法.研究了这两种算法的拟合阶及其为A-稳定的充要条件.最后讨论了四阶导数方法的中间性与误差界.
•  [1] Liniger W.Global accuracy and A-stability of one-and two-step integration formulae forstiff ordinary differential equations[A].In:John,L.Morris Ed.Conference on Numerical Solution of Differential Equations[C],Dundee:Springer-Verlag,1969,188~193. [2] Liniger W,Willoughby R A.Efficient integration methods for stiff systems of ordinary differential equations[J].S I A M J Numer Anal,1970,7(1):47~66. [3] 杨逢建.怎样求函数exp(q)的有理逼近[J].湘潭师范学院学报,1990,10(3):24~32. [4] 李寿佛,杨逢建.函数exp(q)的可接受有理逼近[J].计算数学,1992,14(4):480~488. [5] 袁兆鼎,费景高,刘德贵.刚性常微分方程初值问题的数值解法[M].北京:科学出版社,1987. [6] Lambert J D.Computational Methodsin Ordinary Differential Equations[M].New York:Wiley,1973.

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##### 出版历程
• 收稿日期:  1997-09-11
• 修回日期:  1999-05-08
• 刊出日期:  1999-09-15

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