On Linear Differential-Algebraic Equations and Linearizations

On the background of a careful analysis of linear DAEs, linearizations of nonlinear index2 systems are considered. Finding appropriate function spaces and their topologies allows to apply the standard Implicit Function Theorem again. Both, solvability statements as well as the local convergence of the Newton-Kantorovich method (quasilinearization) result immediately. In particular, this applies also to fully implicit index 1 systems whose leading nullspace is allowed to vary with all its arguments. Keywords. Differential algebraic equations, linearization, Newton-Kantorovich method Introduction Linearization plays an important standard role in the analysis and numerical treatment of regular differential equations. It is a very nice tool for proving solvability statements, showing asymptotic behaviour, describing the sensitivity with respect to parameters etc. Moreover, iterative linearization methods like the standard Newton-Kantorovich method, which is also well-known as quasilinear...