JACOBIAN REUSE IN EXPLICIT INTEGRATORS FOR HIGHER INDEX DAES

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.