BEHAVIOR OF THE NONUNIQUE TERMS IN GENERAL DAE INTEGRATORS

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.