Robust discretizations versus increase of the time step for the Lorenz system

When continuous systems are discretized, their solutions depend on the time step chosen a priori. Such solutions are not necessarily spurious in the sense that they can still correspond to a solution of the differential equations but with a displacement in the parameter space. Consequently, it is of...

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Bibliographic Details
Published inChaos (Woodbury, N.Y.) Vol. 15; no. 1; p. 13110
Main Authors Letellier, Christophe, Mendes, Eduardo M A M
Format Journal Article
LanguageEnglish
Published United States 01.03.2005
Subjects
Algorithms
Fourier Analysis
Models, Statistical
Nonlinear Dynamics
Physics - methods
Time Factors
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Summary:When continuous systems are discretized, their solutions depend on the time step chosen a priori. Such solutions are not necessarily spurious in the sense that they can still correspond to a solution of the differential equations but with a displacement in the parameter space. Consequently, it is of great interest to obtain discrete equations which are robust even when the discretization time step is large. In this paper, different discretizations of the Lorenz system are discussed versus the values of the discretization time step. It is shown that the sets of difference equations proposed are more robust versus increases of the time step than conventional discretizations built with standard schemes such as the forward Euler, backward Euler, or centered finite difference schemes. The nonstandard schemes used here are Mickens' scheme and Monaco and Normand-Cyrot's scheme.
ISSN:1054-1500
1089-7682
DOI:10.1063/1.1865352