Systems F(y', y, t) = 0 with F-y' identically singular are known as di
fferential algebraic equations (DAEs) and occur in a variety of applic
ations. The index nu is one measure of numerical difficulty. Most nume
rical methods for DAEs either require special structure or low index.
Two alternative approaches have been proposed for numerically integrat
ing more general higher index DAEs. This paper examines some of the ma
thematical issues involved in the efficient implementation of the ''ex
plicit integration'' method. It is first shown that the reuse of Jacob
ians can lead to the integration of discontinuous vector fields. It is
then proven that these discontinuous fields can be successfully integ
rated. Computational examples back up the theory. A comparison to a st
andard integrator on an index three control problem illustrates that w
hile the explicit approach can be somewhat more expensive computationa
lly, it can be easier to apply, and does not suffer from order reducti
on in the higher index variables. (C) 1997 Elsevier Science B.V.