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On the mathematically reliable long-term simulation of chaotic solutions of Lorenz equation in the interval [0,10000]

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Abstract

Using 1200 CPUs of the National Supercomputer TH-A1 and a parallel integral algorithm based on the 3500th-order Taylor expansion and the 4180-digit multiple precision data, we have done a reliable simulation of chaotic solution of Lorenz equation in a rather long interval 0 ⩽ t ⩽ 10000 LTU (Lorenz time unit). Such a kind of mathematically reliable chaotic simulation has never been reported. It provides us a numerical benchmark for mathematically reliable long-term prediction of chaos. Besides, it also proposes a safe method for mathematically reliable simulations of chaos in a finite but long enough interval. In addition, our very fine simulations suggest that such a kind of mathematically reliable long-term prediction of chaotic solution might have no physical meanings, because the inherent physical micro-level uncertainty due to thermal fluctuation might quickly transfer into macroscopic uncertainty so that trajectories for a long enough time would be essentially uncertain in physics.

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Authors and Affiliations

  1. State Key Laboratory of Ocean Engineering, Shanghai, 200240, China

    ShiJun Liao

  2. School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    ShiJun Liao

  3. Nonlinear Analysis and Applied Mathematics Research Group (NAAM), King Abdulaziz University (KAU), Jeddah, Saudi Arabia

    ShiJun Liao

  4. State Key Laboratory of Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, 100029, China

    PengFei Wang

Authors
  1. ShiJun Liao
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  2. PengFei Wang
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Correspondence to ShiJun Liao.

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Liao, S., Wang, P. On the mathematically reliable long-term simulation of chaotic solutions of Lorenz equation in the interval [0,10000]. Sci. China Phys. Mech. Astron. 57, 330–335 (2014). https://doi.org/10.1007/s11433-013-5375-z

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  • DOI: https://doi.org/10.1007/s11433-013-5375-z

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