English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Pro

Presents the zaia usage as premium feature

ZAIA

Presents AI Discovery search usage as a premium feature

AI Discovery

Presents AI Discovery explain and summary usage as a premium feature

Content Analysis

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Presents the pdf analysis as premium feature

PDF Analysis

1500 Top-up

3000 Top-up

Zendy Basic

2500 Top-up

Zendy Unlimited

Presents the access of premium content as premium feature

Premium Content

Due to the butterfly-effect, computer-generated chaotic simulations oftendeviate exponentially from the true solution, so that it is very hard to obtaina reliable simulation of chaos in a long-duration time. In this paper, a newstrategy of the so-called Clean Numerical Simulation (CNS) in physical space isproposed for spatio-temporal chaos, which is computationally much moreefficient than its predecessor (in spectral space). The strategy of the CNS isto reduce both of the truncation and round-off errors to a specified level byimplementing high-order algorithms in multiple-precision arithmetic (withsufficient significant digits for all variables and parameters) so as toguarantee that numerical noise is below such a critical level in a temporalinterval $t\in[0,T_c]$ that corresponding numerical simulation remains reliableover the whole interval. Without loss of generality, the complexGinzburg-Landau equation (CGLE) is used to illustrate its validity. As aresult, a reliable long-duration numerical simulation of the CGLE is achievedin the whole spatial domain over a long interval of time $t\in[0,3000]$, whichis used as a reliable benchmark solution to investigate the influence ofnumerical noise by comparing it with the corresponding ones given by the4th-order Runge-Kutta method in double precision (RKwD). Our resultsdemonstrate that the use of double precision in simulations of chaos might leadto huge errors in the prediction of spatio-temporal trajectories and instatistics, not only quantitatively but also qualitatively, particularly in along interval of time.

On the risks of using double precision in numerical simulations of spatio-temporal chaos