Regularization methods for solving differential-algebraic equations

摘要

In [M. Knorrenschild, SIAM J. Numer. Anal. 29 (1992) 1694–1715], a class of regularization methods for solving autonomous index-1 DAEs (differential-algebraic equations) has been proposed. In this paper, we generalize it to non-autonomous index-1 and higher index DAEs. We will treat a DAEs as an infinitely stiff ODEs (ordinary differential equations). Therefore, the solutions of a DAEs can be considered as the limit of the solutions of the corresponding stiff ODEs in some sense. Some similar results with M. Knorrenschild (1992, loc. cit.) are obtained.