Definitions
- Equivalence relation
- Strong Equivalence of matrix pairs
- Regularity of a matrix pair
- Nilpotent matrix, Index of Nilpotency
- Index of a matrix pair
- (global) equivalence of pairs of matrix functions
- (local) equivalence of pairs of matrix functions
- strangeness index
Introduction
- examples of DAEs
- application areas
Basic Concepts
- what is a solution to a DAE?
- what are generally necessary conditions for the existence of a solution?
Linear DAEs with constant coefficients
- Kronecker canonical form
- Kronecker form for regular matrix pairs
- Existence and representation of solutions
Linear DAEs with time varying coefficients
- examples
- quantities
a, d, s, (u, v)
- quantities
r_i, a_i, s_i
- derivative arrays
Numerical Integration of DAEs
- RKM
- how to apply RKM for DAEs
- constant coefficients
- stiffly implicit methods
- nonlinear DAEs
- application examples
- BDF methods
Index Reduction