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Journal of Applied Nonlinear Dynamics 7(2) (2018) 197--204 | DOI:10.5890/JAND.2018.06.008

Shijie Qin$^{1}$, Shijun Liao$^{1}$,$^{2}$

$^{1}$ School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiaotong University, Shanghai, 200240, China

$^{2}$ Ministry-of-Education Key Lab for Scientific and Engineering Computing, Shanghai, 200240, China

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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 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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