REGULAR SOLUTIONS OF NONLINEAR DIFFERENTIAL-ALGEBRAIC EQUATIONS AND THEIR NUMERICAL DETERMINATION

For a general class of nonlinear (possibly higher index) differential- algebraic equations we show existence and uniqueness of solutions. The se solutions are regular in the sense that Newton's method will conver ge locally and quadratically. On the basis of the presented theoretica l results, numerical methods for the determination of consistent initi al values and for the computation of regular solutions are developed. Several numerical examples are included.