We consider general nonlinear index-1 DAEs with properly involved linear derivative term and adress stability topics by means of the structural characterization of those DAEs given in Chapter 4, We investigate contractivity, dissipativity and stability in the sense of Lyapunov, and generalize the classical notions to make sense for DAEs. We provide the related solvability assertions concerning the infinite interval. In particular, an appropriately modified Lyapunov theorem results. We further discuss how integration methods reflect the respective flow properties. We point out that one can benefit from such DAE formulations which show a time-invariant subspace accommodating the derivative term.
KeywordsKutta Method Stability Issue Matrix Pair Dissipativity Inequality Implicit Euler Method
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