How long do numerical chaotic solutions remain valid

@article{Sauer1997HowLD,
  title={How long do numerical chaotic solutions remain valid},
  author={Tim Sauer and Celso Grebogi and James A. Yorke},
  journal={Physical Review Letters},
  year={1997},
  volume={79},
  pages={59-62}
}
Dynamical conditions for the loss of validity of numerical chaotic solutions of physical systems are already understood. However, the fundamental questions of {open_quotes}how good{close_quotes} and {open_quotes}for how long{close_quotes} the solutions are valid remained unanswered. This work answers these questions by establishing scaling laws for the shadowing distance and for the shadowing time in terms of physically meaningful quantities that are easily computable in practice. The scaling… 
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110 Citations
Background Citations
27
Methods Citations
5

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110 Citations

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TLDR
It is shown that the probability distribution of the shadowing time contains two distinct scaling behaviors: an algebraic scaling for short times and an exponential scaling for long times, and the small-time algebraic behavior appears to be universal.
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