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Adaptive interval wavelet precise integration method for partial differential equations

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Abstract

The quasi-Shannon interval wavelet is constructed based on the interpolation wavelet theory, and an adaptive precise integration method, which is based on extrapolation method is presented for nonlinear ordinary differential equations (ODEs). And then, an adaptive interval wavelet precise integration method (AIWPIM) for nonlinear partial differential equations(PDEs) is proposed. The numerical results show that the computational precision of AIWPIM is higher than that of the method constructed by combining the wavelet and the 4th Runge-Kutta method, and the computational amounts of these two methods are almost equal. For convenience, the Burgers equation is taken as an example in introducing this method, which is also valid for more general cases.

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Author information

Authors and Affiliations

  1. College of Information and Electrical Engineering, China Agricultural University, 100083, Beijing, P. R. China

    Mei Shu-li Doctor

  2. School of Sciences, Beijing University of Aeronautics and Astronautics, 100083, Beijing, P. R. China

    Lu Qi-shao Professor & Jin Li

  3. The Institute of Applied Mechanics, Jinan University, 510632, Guangzhou, P. R. China

    Zhang Sen-wen

Authors
  1. Mei Shu-li Doctor
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  2. Lu Qi-shao Professor
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  3. Zhang Sen-wen
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  4. Jin Li
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Corresponding authors

Correspondence to Mei Shu-li Doctor or Lu Qi-shao Professor.

Additional information

Communicated by ZHONG Wan-xie

Project supported by the National Natural Science Foundation of China (Nos. 10372036, 10172011)

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Shu-li, M., Qi-shao, L., Sen-wen, Z. et al. Adaptive interval wavelet precise integration method for partial differential equations. Appl Math Mech 26, 364–371 (2005). https://doi.org/10.1007/BF02440087

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  • DOI: https://doi.org/10.1007/BF02440087

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Chinese Library Classification

2000 Mathematics Subject Classification

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