Transformation of high order linear differential-algebraic systems to first order
- Resource Type
- Authors
- Chunchao Shi; Volker Mehrmann
- Source
- Numerical Algorithms. 42:281-307
- Subject
- Smoothness (probability theory)
Transformation (function)
Applied Mathematics
Numerical analysis
Mathematical analysis
Linear system
Uniqueness
Algebraic number
Differential algebraic equation
Differential (mathematics)
Mathematics
- Language
- ISSN
- 1572-9265
1017-1398
We study general nonsquare linear systems of differential-algebraic systems of arbitrary order. We analyze the classical procedure of turning the system into a first order system and demonstrate that this approach may lead to different solvability results and smoothness requirements. We present several examples that demonstrate this phenomenon and then derive existence and uniqueness results for differential-algebraic systems of arbitrary order and index. We use these results to identify exactly those variables for which the order reduction to first order does not lead to extra smoothness requirements and demonstrate the effects of this new formulation with a numerical example.