Nepomuceno, Erivelton and Martins, Samir A.M. and Silva, Bruno C. and Amaral, Gleison F.V. and Perc, Matjaž (2018) Detecting unreliable computer simulations of recursive functions with interval extensions. Applied Mathematics and Computation, 329. pp. 408-419. ISSN 00963003

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Abstract

This paper presents a procedure to detect unreliable computer simulations of recursive functions. The proposed method calculates a lower bound error which is derived from two different pseudo-orbits based on interval extensions. The interval extensions are generated by taking into account the associative property of multiplication, which keeps the same error bound. We have tested our approach on the logistic map using many different programming languages and simulation packages, including Matlab, Scilab, Octave, Fortran and C. In all cases, the number of iterates is significantly lower than that considered reliable in the existing literature. We have also used the lower bound error on the logistic map and on the polynomial NARMAX for the Rössler equations to estimate the largest Lyapunov exponent, which determines the critical simulation time that guarantees the reliability of the simulation.

Item Type:	Article
Keywords:	Nonlinear dynamics; 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:	16754
Identification Number:	https://doi.org/10.1016/j.amc.2018.02.020
Depositing User:	Erivelton Nepomuceno
Date Deposited:	28 Nov 2022 16:04
Journal or Publication Title:	Applied Mathematics and Computation
Publisher:	Elsevier
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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