Progress on a general numerical method for a numerical method for general implicit differential equations
by
Stephen L. Campbell
Department of Mathematics, North Carolina St. University, Raleigh, NC 27695-8205
Coauthors: Carmen Arevalo (Univ. Simeon Bolivar), Monica Selva (Humboldt University)

Constrained differential equations, or as they are commonly called, differential algebraic equations (DAEs) arise in a number of applications. Classical numerical methods can only be used for special classes of problems. A few years ago, a coordinate partitioning based integrator was proposed which could be used on more general classes of DAEs. While successful, it was difficult to control the global error with this method. This paper will present the latest results on a modification of this approach called Unitary Coordinate Partitioning.

In order to make the results accessible to a larger audience, the paper will briefly review some facts about DAEs and their applications. Then the basic idea behind UCP will be presented. The majority of the talk will carefully discuss new issues that had to be addressed in the actual implementation of this method. The results of computational testing will be presented.

Date received: January 9, 2003