Influence of round-off errors on the reliability of numerical simulations of chaotic dynamic systems
arXiv:1707.04720 · doi:10.5890/JAND.2018.06.008
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.
11 pages, 8 figures, accepted by J. Applied Nonlinear Dynamics