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dc.contributor.authorScott, Joseph Kirk
dc.contributor.authorBarton, Paul I
dc.date.accessioned2017-02-24T23:45:34Z
dc.date.available2017-02-24T23:45:34Z
dc.date.issued2013-03
dc.date.submitted2013-03
dc.identifier.issn0029-599X
dc.identifier.issn0945-3245
dc.identifier.urihttp://hdl.handle.net/1721.1/107162
dc.description.abstractThis article presents two methods for computing interval bounds on the solutions of nonlinear, semi-explicit, index-one differential-algebraic equations (DAEs). Part 1 presents theoretical developments, while Part 2 discusses implementation and numerical examples. The primary theoretical contributions are (1) an interval inclusion test for existence and uniqueness of a solution, and (2) sufficient conditions, in terms of differential inequalities, for two functions to describe componentwise upper and lower bounds on this solution, point-wise in the independent variable. The first proposed method applies these results sequentially in a two-phase algorithm analogous to validated integration methods for ordinary differential equations (ODEs). The second method unifies these steps to characterize bounds as the solutions of an auxiliary system of DAEs. Efficient implementations of both are described using interval computations and demonstrated on numerical examples.en_US
dc.description.sponsorshipNational Science Foundation (U.S.) (grant CBET-0933095)en_US
dc.publisherSpringer Berlin Heidelbergen_US
dc.relation.isversionofhttp://dx.doi.org/10.1007/s00211-013-0532-xen_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alikeen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/en_US
dc.sourceSpringer Berlin Heidelbergen_US
dc.titleInterval bounds on the solutions of semi-explicit index-one DAEs. Part 2: computationen_US
dc.typeArticleen_US
dc.identifier.citationScott, Joseph K., and Paul I. Barton. “Interval Bounds on the Solutions of Semi-Explicit Index-One DAEs. Part 2: Computation.” Numerische Mathematik 125.1 (2013): 27–60.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Chemical Engineeringen_US
dc.contributor.mitauthorScott, Joseph Kirk
dc.contributor.mitauthorBarton, Paul I
dc.relation.journalNumerische Mathematiken_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dc.date.updated2016-05-23T12:09:08Z
dc.language.rfc3066en
dc.rights.holderSpringer-Verlag Berlin Heidelberg
dspace.orderedauthorsScott, Joseph K.; Barton, Paul I.en_US
dspace.embargo.termsNen
dc.identifier.orcidhttps://orcid.org/0000-0003-2895-9443
mit.licenseOPEN_ACCESS_POLICYen_US


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