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Approximation of the viability kernel

dc.contributor.authorSaint-Pierre, Patrick
dc.date.accessioned2015-01-22T09:27:39Z
dc.date.available2015-01-22T09:27:39Z
dc.date.issued1994
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/14596
dc.language.isoenen
dc.subjectViability kernelen
dc.subjectDifferential inclusionsen
dc.subjectNumerical set-valued analysisen
dc.subject.ddc515en
dc.titleApproximation of the viability kernelen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe study recursive inclusionsx n+1 ε G(x n ). For instance, such systems appear for discrete finite-difference inclusionsx n+1 εG ρ (x n) whereG ρ :=1+ρF. The discrete viability kernel ofG ρ , i.e., the largest discrete viability domain, can be an internal approximation of the viability kernel ofK underF. We study discrete and finite dynamical systems. In the Lipschitz case we get a generalization to differential inclusions of the Euler and Runge-Kutta methods. We prove first that the viability kernel ofK underF can be approached by a sequence of discrete viability kernels associated withx n+1 εГ ρ (xn) whereГ ρ (x) =x + ρF(x) + (ML/2) ρ 2ℬ. Secondly, we show that it can be approached by finite viability kernels associated withx h n+1 ε (Г ρ (x h n+1 ) +α(hℬ) ∩X h .en
dc.relation.isversionofjnlnameApplied Mathematics and Optimization
dc.relation.isversionofjnlvol29en
dc.relation.isversionofjnlissue2en
dc.relation.isversionofjnldate1994
dc.relation.isversionofjnlpages187-209en
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/BF01204182en
dc.relation.isversionofjnlpublisherSpringeren
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen


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