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.

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

• Rev Recd Date: 1999-05-08
• Publish Date: 1999-09-15
• By the discussion of the formula and properties of(4,4) parametric form rational approximation to function exp(q),the fourth order derivative one-step exponentially fitted method and the third order derivative hybrid one-step exponentially fitted method are presented,their order p satisfying 6≤p≤8.The necessary and sufficient conditions for the two methods to be A-stable are given.Finally,for the fourth order derivative method,the error bound and the necessary and sufficient conditions for it to be median are discussed.
•  [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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