Differential-Geometric Techniques for Solving Differential Algebraic Equations

Abstract

Differential-algebraic systems of equations (DAEs) arise in many areas of science and engineering. In particular, the equations of motion for a constrained mechanical systems considered in this volume are usually modelled as a second order DAE. In recent years the literature on the numerical solution of such systems has grown rapidly. However, up to now, existence theories for nonlinear DAEs are available only for a few selected classes of systems. The differential-geometric approach is based on the observation that, as long as we expect the solution of a DAE to be some smooth path in the space of dependent variables, the system must define a dynamical system in suitable subsets of that space.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1989
Accession Number
ADA216503

Entities

People

  • Florian A. Potra
  • Werner Rheinboldt

Organizations

  • University of Pittsburgh

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Algorithms
  • Computational Complexity
  • Coordinate Systems
  • Differential Equations
  • Differential Geometry
  • Equations
  • Equations Of Motion
  • Geometry
  • Integrals
  • Intervals
  • Linear Systems
  • Mathematics
  • Molecular Dynamics
  • Nonlinear Systems
  • Statistics
  • Two Dimensional
  • Universities

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space