Solving algebraically explicit DAEs with the MANPAK-manifold-algorithms

Recently, the author introduced a package of algorithms, called MANPAK, for effective computations on implicitly defined submanifolds of n. Here algebraically explicit differential algebraic equations (DAEs) are considered; that is, DAEs in which either the algebraic equations and/or the algebraic variables are explicitly specified. Existence proofs for several types of such DAEs of index one, two, and three are given, which directly suggest computational approaches. This is used in the development of solution algorithms for these DAEs, all of them intrinsically based on the MANPAK routines. Some numerical examples for the methods are included.