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

TL;DR

This paper demonstrates that round-off errors significantly impact the reliability of long-term numerical simulations of chaotic systems, emphasizing the need for minimizing both truncation and round-off errors for accurate results.

Contribution

It highlights the importance of controlling round-off errors alongside truncation errors to improve the reliability of chaotic system simulations.

Findings

Round-off errors significantly affect simulation reliability.

Reducing errors requires using smaller truncation and round-off levels.

Verification with even smaller errors enhances confidence in results.

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.