The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc.
Aalto

Numerical Solution and Structural Analysis of Differential-Algebraic Equations

Teijo Arponen

Dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the Department of Engineering Physics and Mathematics, for public examination and debate in Lecture Hall G at Helsinki University of Technology (Espoo, Finland) on the 18th of June, 2002, at 12 noon.

Overview in PDF format (ISBN 951-22-5909-5)   [285 KB]
Dissertation is also available in print (ISBN 951-22-5953-2)

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.

This thesis consists of an overview and of the following 4 publications:

  1. J. Tuomela and T. Arponen. On the numerical solution of involutive ordinary differential systems. IMA J. Numer. Anal., 20:561-599, 2000.
  2. J. Tuomela and T. Arponen. On the numerical solution of involutive ordinary differential systems: higher order methods. BIT, 41:599-628, 2001. © 2001 BIT. By permission.
  3. T. Arponen. Regularization of constraint singularities in multibody systems. Multibody Systems Dynamics, 6:355-375, 2001.
  4. T. Arponen. The complete form of a differential algebraic equation. Revised version of Technical Report A438, Helsinki University of Technology, 2001. Submitted. © 2001 by author.

Keywords: symbolic computation, Runge-Kutta methods, index reduction, overdetermined differential equations

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© 2002 Helsinki University of Technology

Last update 2011-05-26