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Lacerda Junior, Wilson R., 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: | 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 |
| Related URLs: | |
| URI: | https://mural.maynoothuniversity.ie/id/eprint/16760 |
| 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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