Numerical solution and structural analysis of differential-algebraic equations
Loading...
URL
Journal Title
Journal ISSN
Volume Title
Doctoral thesis (article-based)
Checking the digitized thesis and permission for publishing
Instructions for the author
Instructions for the author
Unless otherwise stated, all rights belong to the author. You may download, display and print this publication for Your own personal use. Commercial use is prohibited.
Authors
Date
Major/Subject
Mcode
Degree programme
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.Description
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.