Geometric Properties of Runge-Kutta Discretizations for Nonautonomous Index 2 Differential Algebraic Systems

Geometric Properties of Runge-Kutta Discretizations for Index 2 Differential Algebraic Systems

Geometric Properties of Runge-Kutta Discretizations for Index 2 Differential Algebraic Systems

Behavior of Runge-Kutta Discretizations near equilibria of Index 2 Differential Algebraic Systems

Invariant manifolds in differential algebraic equations of index 3 and in their Runge-Kutta discretizations

Partitioned Runge-Kutta Methods for Semi-explicit Differential-Algebraic Systems of Index 2

A general class of one-step methods for index 2 differential-algebraic systems in Hessenberg form is studied. This family of methods, which we call partitioned Runge-Kutta methods, includes all one-step methods of Runge-Kutta type proposed in the literature for integrating such DAE systems, including the more recently proposed classes of half-explicit methods. A new family of super-convergent p...