Daes That Should Not Be Solved

The closing decades of the 20th century have seen many scientists recognize that their mathematical models are in fact instances of DAEs, or of ODEs with invariants. Such a recognition has often carried with it the beneet of aaording a new, sometimes revealing, computational look at the old problem. But one must not conclude that reformulating a mathematical model as a DAE is always a good idea. Neither should one automatically assume that a numerical approximation of a diierential system with an invariant must respect the invariant rst, and only then worry about discretizing the diierential equations. In this article we give some examples to the contrary: enforcing energy conservation in highly oscillatory Hamiltonian systems; moving meshes for PDEs; and reproducing an entire homotopy path as a way for reaching its end.