A General Existence and Uniqueness Theorem for Implicit Differential- Algebraic Equations
Abstract
This paper presents a general existence and uniqueness theory for differential-alegebraic equations extending the well known ODE theory. Both local and global aspects are considered, and the definition of the index for nonlinear problems is elucidated. For the case of linear problems with constant coefficients the results are shown to provide an alternate treatment equivalent to the standard approach in terms of matrix pencils. Also, it is proved that general differential-algebraic equations carry a geometric content, in that they are locally equivalent to ODEs on a constraint manifold. A simple example from particle dynamics is given to illustrate our approach. (KR)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1990
- Accession Number
- ADA217965
Entities
People
- Patrick J. Rabier
- Werner Rheinboldt
Organizations
- University of Pittsburgh