title: Robust discretizations versus increase of the time step for the Lorenz system.
abstract: 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.
authors.affiliation: CORIA UMR 6614, Université de Rouen, Av. de l'Université, Boîte Postale 12, F-76801 Saint-Etienne du Rouvray cedex, France. christophe.letellier@coria.fr
authors.forename: Christophe
authors.initials: C
authors.lastname: Letellier
authors.forename: Eduardo M A M
authors.initials: EM
authors.lastname: Mendes
mesh_terms: D000465:Algorithms; D005583:Fourier Analysis; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D010825:Physics / Q000379:methods; D013997:Time Factors