document: Behavior of Runge-Kutta discretizations near equilibria of index 2 differential algebraic systems We analyze Runge-Kutta discretizations applied to index 2 differential algebraic equations -LRB- DAE 's -RRB- near equilibria . We compare the geometric properties of the numerical and the exact solutions . It is shown that projected and half-explicit Runge-Kutta methods reproduce the qualitative features of the continuous system in the vicinity of an equilibrium correctly . The proof combines cut-off and scaling techniques for index 2 differential algebraic equations with some invariant manifold results of Schropp -LRB- Geometric properties of Runge-Kutta discretizations for index 2 differential algebraic equations , Konstanzer Schriften in Mathematik und Informatik 128 -RRB- and classical results for discretized ordinary differential equations
doc_bio_tags: O O O O O B O B I I I I O O O O O O O O O O O O O O O O B O O O O B I O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O B I O O O O O O O O B I O O O O B I O O O O O O O O O O O O O O O O O O O O O O B I I I
extractive_keyphrases: index 2 differential algebraic systems equilibria geometric properties continuous system scaling techniques invariant manifold discretized ordinary differential equations
abstractive_keyphrases: runge-kutta discretizations half-explicit runge-kutta methods cut-off techniques