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dc.contributor.authorGameiro, M.
dc.contributor.authorLessard, J.-P.
dc.date.accessioned2017-02-21T08:19:28Z
dc.date.available2017-02-21T08:19:28Z
dc.date.issued2013-12-31
dc.identifier.issn0036-1429
dc.identifier.urihttp://hdl.handle.net/20.500.11824/612
dc.description.abstractWe present an efficient rigorous computational method which is an extension of the work Analytic Estimates and Rigorous Continuation for Equilibria of Higher-Dimensional PDEs (M. Gameiro and J.-P. Lessard, J. Differential Equations, 249 (2010), pp. 2237-2268). The idea is to generate sharp one-dimensional estimates using interval arithmetic which are then used to produce high-dimensional estimates. These estimates are used to construct the radii polynomials which provide an efficient way of determining a domain on which the contraction mapping theorem is applicable. Computing the equilibria using a finite-dimensional projection, the method verifies that the numerically produced equilibrium for the projection can be used to explicitly define a set which contains a unique equilibrium for the PDE. A new construction of the polynomials is presented where the nonlinearities are bounded by products of one-dimensional estimates as opposed to using FFT with large inputs. It is demonstrated that with this approach it is much cheaper to prove that the numerical output is correct than to recompute at a finer resolution. We apply this method to PDEs defined on three- and four-dimensional spatial domains.
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.subjectComputer assisted proofs
dc.subjectEquilibria of PDEs
dc.subjectHigher-dimensional PDEs
dc.subjectRigorous numerics
dc.titleEfficient rigorous numerics for higher-dimensional PDEs via one-dimensional estimatesen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.identifier.doi10.1137/110836651
dc.relation.publisherversionhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-84888871330&doi=10.1137%2f110836651&partnerID=40&md5=97e655cb9fa78f9f29f0b298a8e26e22
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/publishedVersionen_US
dc.journal.titleSIAM Journal on Numerical Analysisen_US


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Reconocimiento-NoComercial-CompartirIgual 3.0 España
Except where otherwise noted, this item's license is described as Reconocimiento-NoComercial-CompartirIgual 3.0 España