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

• 论文 • 上一篇    下一篇

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

杨逢建1, 张爱国2, 陈新明3   

  1. 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
  • 收稿日期:1997-09-11 修回日期:1999-05-08 出版日期:1999-09-18 发布日期:1999-09-18
  • 基金资助:

    the Science Technology Foundation of Ministry of Machine-Buildin Industry of China(96252011)

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

Yang Fengjian1, Zhang Aiguo2, Chen Xinming3   

  1. 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)

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摘要： 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.

关键词: exponentially fitted method, order, A-stability

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

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