A Geometric Treatment of Implicit Differential-Algebraic Equations

Abstract

A differential geometric approach for proving the existence and uniqueness of solutions of implicit differential algebraic equations is presented. It provides for a significant improvement of an earlier theory developed by the authors as well as for a completely intrinsic definition of the index of such problems. The differential algebraic equation is transformed into an explicit ordinary differential equation by a reduction process that can be abstractly defined for specific submanifolds of tangent bundles here called reducible pi-submanifolds. Local existence and uniqueness results for differential-algebraic equations then follow directly from the final stage of this reduction by means of an application of the standard theory of ordinary differential equations.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1991
Accession Number
ADA236991

Entities

People

  • Patrick J. Rabier
  • Werner Rheinboldt

Organizations

  • University of Pittsburgh

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Coordinate Systems
  • Decomposition
  • Differential Equations
  • Equations
  • Intervals
  • Linear Systems
  • Mathematics
  • Notation
  • Pendulums
  • Sequences
  • Standards
  • Stationary
  • Statistics
  • Three Dimensional
  • Two Dimensional
  • Universities

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Graph Algorithms and Convex Optimization.