Convergence Criterium of Numerical Chaotic Solutions Based on Statistical Measures
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 di...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2011 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/101960 |
| Acceso en línea: | http://hdl.handle.net/11336/101960 |
| Access Level: | acceso abierto |
| Palabra clave: | Chaotic Attractor Statistical Measure Numerical Integration https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | 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. |
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