ON CONSTRUCTION OF HIGH ORDER EXPONENTIALLY FITTED METHODS BASED ON PARAMETERIZED RATIONAL APPROXIMATIONS TO exp(q)

Applied Mathematics and Mechanics (English Edition) ›› 1999, Vol. 20 ›› Issue (9): 1023-1030.

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ON CONSTRUCTION OF HIGH ORDER EXPONENTIALLY FITTED METHODS BASED ON PARAMETERIZED RATIONAL APPROXIMATIONS TO exp(q)

Yang Fengjian¹, Zhang Aiguo², Chen Xinming³

1. Zhongkai Agrotechnical College, Guangzhou 510225, P. R. China;
2. Xiangtan Institute of Machinery and Electricity, Xiangtan 411101, P. R. China;
3. Department of Mathematics and Physics, Wuyi University, Jiangmen 529042, P. R. China

Received:1997-09-11 Revised:1999-05-08 Online:1999-09-18 Published:1999-09-18
Supported by:
the Science Technology Foundation of Ministry of Machine-Buildin Industry of China(96252011)

Abstract

Abstract: 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.

Key words: exponentially fitted method, order, A-stability

2010 MSC Number:

Yang Fengjian;Zhang Aiguo;Chen Xinming. ON CONSTRUCTION OF HIGH ORDER EXPONENTIALLY FITTED METHODS BASED ON PARAMETERIZED RATIONAL APPROXIMATIONS TO exp(q). Applied Mathematics and Mechanics (English Edition), 1999, 20(9): 1023-1030.

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ON CONSTRUCTION OF HIGH ORDER EXPONENTIALLY FITTED METHODS BASED ON PARAMETERIZED RATIONAL APPROXIMATIONS TO exp(q)

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