Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the risks of using double precision in numerical simulations of
  spatio-temporal chaos   Due to the butterfly-effect, computer-generated chaotic simulations often
deviate exponentially from the true solution, so that it is very hard to obtain
a reliable simulation of chaos in a long-duration time. In this paper, a new
strategy of the so-called Clean Numerical Simulation (CNS) in physical space is
proposed for spatio-temporal chaos, which is computationally much more
efficient than its predecessor (in spectral space). The strategy of the CNS is
to reduce both of the truncation and round-off errors to a specified level by
implementing high-order algorithms in multiple-precision arithmetic (with
sufficient significant digits for all variables and parameters) so as to
guarantee that numerical noise is below such a critical level in a temporal
interval $t\in[0,T_c]$ that corresponding numerical simulation remains reliable
over the whole interval. Without loss of generality, the complex
Ginzburg-Landau equation (CGLE) is used to illustrate its validity. As a
result, a reliable long-duration numerical simulation of the CGLE is achieved
in the whole spatial domain over a long interval of time $t\in[0,3000]$, which
is used as a reliable benchmark solution to investigate the influence of
numerical noise by comparing it with the corresponding ones given by the
4th-order Runge-Kutta method in double precision (RKwD). Our results
demonstrate that the use of double precision in simulations of chaos might lead
to huge errors in the prediction of spatio-temporal trajectories and in
statistics, not only quantitatively but also qualitatively, particularly in a
long interval of time.

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The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex