Quasi-linear differential-algebraic equations is a convenient model structure
for dynamical systems. Such models generally contain both exactly known and
uncertain coefficients. The structure that the exactly known coefficients
adds to the equations can be utilized when analyzing or solving the
equations, but requires a more detailed model structure than general DAE.
When developing theory and/or software for DAE, one needs to decide what
additional structure to impose on the equations, and it is tempting to take
on as general forms as possible, both to gain wide applicability and to avoid
the extra bookkeeping that any additional structure would require.
In this talk, the consequences of neglecting the structure that exactly known
coefficients bring to the equations will be discussed. The resulting problem
will also be motivated by symbolic-numeric approaches to integration of
exactly known systems, and a general approach to tackle it will be presented.
In view of available results, it is also motivated to question the use of
unstructured DAE as a model structure.