Year: 2023
Author: Shijie Qin, Shijun Liao
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 5 : pp. 1191–1215
Abstract
The background numerical noise $ε_0$ is determined by the maximum of truncation error and round-off error. For a chaotic system, the numerical error $ε(t)$ grows exponentially, say, $ε(t) = ε_0 {\rm exp}(κt),$ where $κ > 0$ is the so-called noise-growing exponent. This is the reason why one can not gain a convergent simulation of chaotic systems in a long enough interval of time by means of traditional algorithms in double precision, since the background numerical noise $ε_0$ might stop decreasing because of the use of double precision. This restriction can be overcome by means of the clean numerical simulation (CNS), which can decrease the background numerical noise $ε_0$ to any required tiny level. A lot of successful applications show the novelty and validity of the CNS. In this paper, we further propose some strategies to greatly increase the computational efficiency of the CNS algorithms for chaotic dynamical systems. It is highly suggested to keep a balance between truncation error and round-off error and besides to progressively enlarge the background numerical noise $ε_0,$ since the exponentially increasing numerical noise $ε(t)$ is much larger than it. Some examples are given to illustrate the validity of our strategies for the CNS.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2022-0340
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 5 : pp. 1191–1215
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Chaos Clean Numerical Simulation (CNS) self-adaptive algorithm computational efficiency.