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dc.contributor.authorIgnat, L.I.
dc.contributor.authorZuazua, E.
dc.date.accessioned2017-02-21T08:18:19Z
dc.date.available2017-02-21T08:18:19Z
dc.date.issued2012-12-31
dc.identifier.issn0021-7824
dc.identifier.urihttp://hdl.handle.net/20.500.11824/553
dc.description.abstractThis article is devoted to the analysis of the convergence rates of several numerical approximation schemes for linear and nonlinear Schrödinger equations on the real line. Recently, the authors have introduced viscous and two-grid numerical approximation schemes that mimic at the discrete level the so-called Strichartz dispersive estimates of the continuous Schrödinger equation. This allows to guarantee the convergence of numerical approximations for initial data in L2(R), a fact that cannot be proved in the nonlinear setting for standard conservative schemes unless more regularity of the initial data is assumed. In the present article we obtain explicit convergence rates and prove that dispersive schemes fulfilling the Strichartz estimates are better behaved for Hs(R) data if 0 < s< 1/2. Indeed, while dispersive schemes ensure a polynomial convergence rate, non-dispersive ones only yield logarithmic ones.
dc.formatapplication/pdf
dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectError analysis
dc.subjectFinite differences
dc.subjectNonlinear Schrödinger equation
dc.subjectStrichartz estimates
dc.titleConvergence rates for dispersive approximation schemes to nonlinear Schrödinger equations
dc.typeinfo:eu-repo/semantics/articleen_US
dc.identifier.doi10.1016/j.matpur.2012.01.001
dc.relation.publisherversionhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-84867329128&doi=10.1016%2fj.matpur.2012.01.001&partnerID=40&md5=364fe8f978dddb17eceb694f00a7007c
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/publishedVersionen_US
dc.journal.titleJournal des Mathematiques Pures et Appliqueesen_US


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