We propose an analysis of the effects introduced by finite accuracy and round-off arithmetic on discrete dynamical systems. We investigate, from a statistical viewpoint and using the tool of the decay of fidelity, the error of the numerical orbit with respect to the exact one. As a model we consider a random perturbation of the exact orbit with an additive noise, for which exact results can be obtained for some prototype maps. For regular anysocrounous maps the fidelity has a power law decay, whereas the decay is exponential if a random perturbation is introduced. For chaotic maps the decay is superexponential after an initial plateau and our method is suitable to identify the reliability threshold of numerical results, i.e. a number of iterations below which global errors can be ignored. The same behaviour is observed if a random perturbation is introduced.
Turchetti G, Vaienti S, Zanlungo F (2010). Relaxation to the asymptotic distribution of global errors due to round off. EUROPHYSICS LETTERS [10.1209/0295-5075/89/40006].
Relaxation to the asymptotic distribution of global errors due to round off
Zanlungo F
2010-03-05
Abstract
We propose an analysis of the effects introduced by finite accuracy and round-off arithmetic on discrete dynamical systems. We investigate, from a statistical viewpoint and using the tool of the decay of fidelity, the error of the numerical orbit with respect to the exact one. As a model we consider a random perturbation of the exact orbit with an additive noise, for which exact results can be obtained for some prototype maps. For regular anysocrounous maps the fidelity has a power law decay, whereas the decay is exponential if a random perturbation is introduced. For chaotic maps the decay is superexponential after an initial plateau and our method is suitable to identify the reliability threshold of numerical results, i.e. a number of iterations below which global errors can be ignored. The same behaviour is observed if a random perturbation is introduced.File | Dimensione | Formato | |
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