Reversible methods of Runge-Kutta type for index-2 DAEs (Q1889953)

The behavior of implicit Runge-Kutta type schemes applied to reversible or symmetric index-2 differential algebraic equations (DAEs) is investigated. The authors show that these schemes maintain the full convergence order from the ordinary differential equations situation when combined with a symmetric or a post-projection. Moreover, the geometric phase portrait is correctly reproduced. This means that the discrete step forward map of a symmetric or reversible index-2 equation is symmetric or reversible, respectively. Finally, the power of the method is demonstrated for the well known double pendulum problem.