de Figueiredo, Julio Cesar Bastos and Diambra, Luis and Malta, Coraci Pereira (2011) Convergence Criterium of Numerical Chaotic Solutions Based on Statistical Measures. Applied Mathematics, 02 (04). pp. 436-443. ISSN 2152-7385
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Abstract
Solutions of most nonlinear differential equations have to be obtained numerically. The time series obtained by numerical integration will be a solution of the differential equation only if it is independent of the integration step h. A numerical solution is considered to have converged, when the difference between the time series for steps h and h/2 becomes smaller as h decreases. Unfortunately, this convergence criterium is unsuitable in the case of a chaotic solution, due to the extreme sensitivity to initial conditions that is characteristic of this kind of solution. We present here a criterium of convergence that involves the comparison of the attractors associated to the time series for integration time steps h and h/2. We show that the probability that the chaotic attractors associated to these time series are the same increases monotonically as the integration step h is decreased. The comparison of attractors is made using 1) the method of correlation integral, and 2) the method of statistical distance of probability distributions.
Item Type: | Article |
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Subjects: | Euro Archives > Mathematical Science |
Depositing User: | Managing Editor |
Date Deposited: | 08 Jun 2023 06:30 |
Last Modified: | 28 Oct 2023 03:52 |
URI: | http://publish7promo.com/id/eprint/2669 |