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Detecting unreliable computer simulations of recursive functions with interval extensions

Author

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

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.

Suggested Citation

  • Nepomuceno, Erivelton G. & Martins, Samir A.M. & Silva, Bruno C. & Amaral, Gleison F.V. & Perc, Matjaž, 2018. "Detecting unreliable computer simulations of recursive functions with interval extensions," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 408-419.
    • Handle: RePEc:eee:apmaco:v:329:y:2018:i:c:p:408-419
    DOI: 10.1016/j.amc.2018.02.020
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    References listed on IDEAS

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    1. Nepomuceno, Erivelton Geraldo & Mendes, Eduardo M.A.M., 2017. "On the analysis of pseudo-orbits of continuous chaotic nonlinear systems simulated using discretization schemes in a digital computer," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 21-32.
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    Cited by:

    1. Nardo, Lucas G. & Nepomuceno, Erivelton G. & Arias-Garcia, Janier & Butusov, Denis N., 2019. "Image encryption using finite-precision error," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 69-78.
    2. Nepomuceno, Erivelton G. & Rodrigues Junior, Heitor M. & Martins, Samir A.M. & Perc, Matjaž & Slavinec, Mitja, 2018. "Interval computing periodic orbits of maps using a piecewise approach," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 67-75.
    3. Guedes, Priscila F.S. & Mendes, Eduardo M.A.M. & Nepomuceno, Erivelton, 2022. "Effective computational discretization scheme for nonlinear dynamical systems," Applied Mathematics and Computation, Elsevier, vol. 428(C).

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