Regularization of DAEs based on the signature method (Q285293)

In this well-written paper, the authors present a new regularizing method for nonlinear high-index differential-algebraic equations, (DAEs) which often arise as the results of automated modeling of multi-physics dynamical systems. Direct numerical simulation of high-index DAEs usually leads to instabilities and non-convergence of the numerical methods. Thus, a regularization or remodeling is needed. In order to get an index-reduced model, the structural analysis approach is preferable to the classical algebraic approach. Here, the authors follow the structural analysis approach and propose a procedure that is based on the signature method (\(\varSigma\)-method), see [\textit{J. D. Pryce}, BIT 41, No. 2, 364--394 (2001; Zbl 0989.34005)]. The main result is presented in Theorem 3. In a constructive way, by differentiating the original system and by introducing new variables appropriately, an augmented regular system is obtained which has a differentiation index \(\nu_d\leq 1\) (i.e., the strangeness index \(\mu=0\)). A comparison of this method with the method of dummy derivatives, see [\textit{S. E. Mattsson} and \textit{G. Söderlind}, SIAM J. Sci. Comput. 14, No. 3, 677--692 (1993; Zbl 0785.65080)], is discussed. Examples are also given for illustration.