Lacerda Junior, Wilson R. and Martins, Samir A.M. and Nepomuceno, Erivelton (2018) The lower bound error as an auxiliary technique to select the integration step-size in the simulation of chaotic systems. Learning and Nonlinear Models, 16 (1). pp. 56-67. ISSN 1676-2789

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Abstract

This work presents a method to choose the integration step-size h for discretization of nonlinear and chaotic dynamic systems, in order to obtain a simulation with numerical reliability. In this context, the Lower Bound Error is used as an auxiliary technique in the search for the optimal value of h, considering the Fourth Order Runge Kutta as the discretization method. The Lorenz equations, R¨ossler equations and Duffing-Ueda oscillator were used as case studies. This work, besides investigating the most adequate step-size h for each case, shows that the choice of very small values of h results in significantly inferior solutions, despite the consensus that the smaller the step-size, the higher the accuracy.

Item Type:	Article
Keywords:	dynamical system; discrete time systems; chaos; numerical simulation; lower bound error;
Academic Unit:	Faculty of Science and Engineering > Electronic Engineering Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID:	16760
Identification Number:	https://doi.org/10.21528/LNLM-vol16-no1-art4
Depositing User:	Erivelton Nepomuceno
Date Deposited:	29 Nov 2022 16:43
Journal or Publication Title:	Learning and Nonlinear Models
Publisher:	Springer Open
Refereed:	Yes
URI:	Publisher
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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