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    The lower bound error as an auxiliary technique to select the integration step-size in the simulation of chaotic systems


    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:

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