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arXiv · 1707.04720

Influence of round-off errors on the reliability of numerical simulations of chaotic dynamic systems

Shijie Qin·Shijun Liao
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Abstract

We illustrate that, like the truncation error, the round-off error has a significant influence on the reliability of numerical simulations of chaotic dynamic systems. Due to the butterfly-effect, all numerical approaches in double precision cannot give a reliable long-term simulation of chaotic dynamic systems. So, in order to avoid man-made uncertainty of numerical simulations of chaos, we had to greatly decrease both of the truncation and round-off error to a small enough level, plus a verification of solution reliability by means of an additional computation using even smaller truncation and round-off errors.

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Shijie Qin, Shijun Liao. 2017-07-15. Influence of round-off errors on the reliability of numerical simulations of chaotic dynamic systems. https://doi.org/10.5890/jand.2018.06.008

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