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On the mathematically reliable long-term simulation of chaotic solutions of Lorenz equation in the interval [0,10000]
Source: LASG     Viewed:  time(s) 
Authors
LIAO Shijun, WANG Pengfei, ,
Journal
 Science China Physics, Mechanics and Astronomy
Year
2014
Page number
57: 330-335
Key words
 chaos, reliable simulation, uncertainty propagation
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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