Differential algebraic equations (DAEs) are implicit systems of ordina
ry differential equations F (y', y, t) = 0. DAEs arise in many applica
tions and a variety of numerical methods have been developed for solvi
ng DAEs. Numerical methods have been proposed for integrating general
higher index DAEs and successfully applied to test problems. These met
hods require solving a nonlinear system of equations which is larger t
han the original DAE at each time step. For fully implicit problems pa
rt of the solution of the nonlinear system is not uniquely determined.
This poses questions about the effects of predictors and also a possi
ble instability in the growth of these terms during a numerical integr
ation. In this paper it is shown that the nonunique component is actua
lly the numerical solution of an auxiliary DAE which depends not only
on the original DAE but also on the predictor being used in the Gauss-
Newton iteration. As an important consequence we both establish a basi
s for the design of low order integrators for high index DAEs and deve
lop guidelines for the use of predictors in integrating general high i
ndex DAEs. (C) 1998 Elsevier Science B.V. and IMACS. All rights reserv
ed.