Detecting unreliable computer simulations of recursive functions with interval extensions

Erivelton G. Nepomuceno, Samir A.M. Martins, Bruno C. Silva, Gleison F.V. Amaral and Matjaž Perc

Applied Mathematics and Computation, 2018, vol. 329, issue C, 408-419

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.

Keywords: Nonlinear dynamics; Chaos; Numerical simulation; Lower bound error (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:329:y:2018:i:c:p:408-419

DOI: 10.1016/j.amc.2018.02.020

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