Behavior of Runge–Kutta discretizations near equilibria of index 2 differential algebraic systems Original Research Article

We analyze Runge–Kutta discretizations applied to index 2 differential algebraic equations (DAEʹs) 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 [J. Schropp, Geometric properties of Runge–Kutta discretizations for index 2 differential algebraic equations, Konstanzer Schriften in Mathematik und Informatik 128] and classical results for discretized ordinary differential equations.