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

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

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

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

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

Projected Runge-kutta Methods for Differential Algebraic Equations of Index 3

In the present paper we introduce a new class of methods, Projected RungeKutta methods, for the solution of index 3 differential algebraic equations (DAEs) in Hessenberg form. The methods admit the integration of index 3 DAEs without any drift effects. This makes them particularly well suited for long term integration. Finally, implemented on the basis of the Radau5 code, the projected Runge-Ku...