Numerical solution and structural analysis of differential-algebraic equations

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Doctoral thesis (article-based)
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Date
2002-06-18
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Language
en
Pages
22, [111]
Series
Research reports / Helsinki University of Technology, Institute of Mathematics. A, 409
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.
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Keywords
symbolic computation, Runge-Kutta methods, index reduction, overdetermined differential equations
Other note
Parts
  • J. Tuomela and T. Arponen. On the numerical solution of involutive ordinary differential systems. IMA J. Numer. Anal., 20:561-599, 2000.
  • 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.
  • T. Arponen. Regularization of constraint singularities in multibody systems. Multibody Systems Dynamics, 6:355-375, 2001.
  • 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.
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Permanent link to this item
https://urn.fi/urn:nbn:fi:tkk-001557