Least squares completions for nonlinear differential algebraic equations

Summary A method has been proposed for numerically solving lower dimensional, nonlinear, higher index differential algebraic equations for which more classical methods such as backward differentiation or implicit Runge-Kutta may not be appropriate. This method is based on solving nonlinear DAE derivative arrays using nonlinear singular least squares methods. The theoretical foundations, generality, and limitations of this approach remain to be determined. This paper carefully examines several key aspects of this approach. The emphasis is on general results rather than specific results based on the structure of various applications.Research supported in part by the U.S. Army Research Office under DAALO3-89-D-0003 and the National Science Foundation under ECS-9012909 and DMS-9122745