Numerical solution and structural analysis of differential-algebraic equations

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dc.contributor Aalto-yliopisto fi
dc.contributor Aalto University en
dc.contributor.author Arponen, Teijo
dc.date.accessioned 2012-02-10T09:22:35Z
dc.date.available 2012-02-10T09:22:35Z
dc.date.issued 2002-06-18
dc.identifier.isbn 951-22-5909-5
dc.identifier.issn 0784-3143
dc.identifier.uri https://aaltodoc.aalto.fi/handle/123456789/2185
dc.description.abstract In the last two decades differential-algebraic equations (DAEs) have become an important branch in numerical analysis. In this Thesis we study them from a new, geometric point of view. The DAE is interpreted as a subset of a jet bundle and its solution are induced by the Cartan distribution on the jet bundle. We also introduce a method to examine and define the structure of a general, polynomial, DAE whose locus is not necessarily a fibred manifold. Also it is shown how some singularities of multibody systems are removed by using the algebraic techniques used in this approach. en
dc.format.extent 22, [111]
dc.format.mimetype application/pdf
dc.language.iso en en
dc.publisher Helsinki University of Technology en
dc.publisher Teknillinen korkeakoulu fi
dc.relation.ispartofseries Research reports / Helsinki University of Technology, Institute of Mathematics. A en
dc.relation.ispartofseries 409 en
dc.relation.haspart J. Tuomela and T. Arponen. On the numerical solution of involutive ordinary differential systems. IMA J. Numer. Anal., 20:561-599, 2000.
dc.relation.haspart J. Tuomela and T. Arponen. On the numerical solution of involutive ordinary differential systems: higher order methods. BIT, 41:599-628, 2001. [article2.pdf] © 2001 BIT. By permission.
dc.relation.haspart T. Arponen. Regularization of constraint singularities in multibody systems. Multibody Systems Dynamics, 6:355-375, 2001.
dc.relation.haspart T. Arponen. The complete form of a differential algebraic equation. Revised version of Technical Report A438, Helsinki University of Technology, 2001. Submitted. [article4.pdf] © 2001 by author.
dc.subject.other Mathematics en
dc.title Numerical solution and structural analysis of differential-algebraic equations en
dc.type G5 Artikkeliväitöskirja fi
dc.description.version reviewed en
dc.contributor.department Department of Engineering Physics and Mathematics en
dc.contributor.department Teknillisen fysiikan ja matematiikan osasto fi
dc.subject.keyword symbolic computation en
dc.subject.keyword Runge-Kutta methods en
dc.subject.keyword index reduction en
dc.subject.keyword overdetermined differential equations en
dc.identifier.urn urn:nbn:fi:tkk-001557
dc.type.dcmitype text en
dc.type.ontasot Väitöskirja (artikkeli) fi
dc.type.ontasot Doctoral dissertation (article-based) en
dc.contributor.lab Institute of Mathematics en
dc.contributor.lab Matematiikan laitos fi


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