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On construction of high order exponentially fitted methods based on parameterized rational approximations to exp(q)

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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.

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References

  1. Liniger W. Global accuracy andA-stability of one-and two-step integration formulae for stiff ordinary differential equations [A]. In: John, L. Morris Ed,Conference on Numerical Solution of Differential Equations [C], Dundee: Springer-Verlag, 1969, 188–193.

    Chapter  Google Scholar 

  2. Liniger W, Willoughby R A. Efficient integration methods for stiff systems of ordinary differential equations [J].SIAM J Numer Anal, 1970,7 (1): 47–66.

    Article  MathSciNet  Google Scholar 

  3. Yang Fengjian. How we obtain acceptble rational approximations to exp (q) [J].Journal of Xiangtan Teachers College, 1990,10 (3): 24–32. (in Chinese)

    Google Scholar 

  4. Li Shoufo, Yang Fengjian. Acceptability of rational approximations to the function exp (q) [J].Mathematica Numerica Sinica, 1992,14 (4): 480–488. (in Chinese)

    Google Scholar 

  5. Yuan Zhaoding, Fei Jinggao, Liu Degui,Numerical Methods for Initial Value Problems of Stiff Ordinary Differential Equations [M]. Beijing: Science Publishing House, 1987. (in Chinese)

    Google Scholar 

  6. Lambert J DComputational Methods in Ordinary Differential Equations [M]. New York: Wiley, 1973.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Zhongkai Agrotechnical College, 510225, Guangzhou, P R China

    Yang Fengjian

  2. Xiangtan Institute of Machinery and Electricity, 411101, Xiangtan, P R China

    Zhang Aiguo

  3. Department of Mathematics and Physics, Wuyi University, 529042, Jiangmen, P R China

    Chen Xinming

Authors
  1. Yang Fengjian
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  2. Zhang Aiguo
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  3. Chen Xinming
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Additional information

Communicated by Lin Zongchi

Foundation item: the Science Technology Foundation of Ministry of Machine-Building Industry of China (96252011)

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Fengjian, Y., Aiguo, Z. & Xinming, C. On construction of high order exponentially fitted methods based on parameterized rational approximations to exp(q). Appl Math Mech 20, 1023–1030 (1999). https://doi.org/10.1007/BF02459066

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  • DOI: https://doi.org/10.1007/BF02459066

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