On the global error of special Runge–Kutta methods applied to linear Differential Algebraic Equations

Global error estimates are obtained for Runge-Kutta methods of special type when applied to linear constant coefficient Differential Algebraic Equations (DAEs) of arbitrary high index ν≥0. A Runge-Kutta formula is said of special type when its first internal stage is computed explicitly, the remaining internal stages are obtained in terms of a regular coefficient submatrix whereas the last internal stage equals the advancing solution. As a main result, one extra order of convergence on arbitrary high index ν≥2 linear constant coefficient DAEs is obtained for a one parameter family of strictly stable Runge-Kutta collocation methods of special type when compared to the classical Radau IIA formulae for the same number of implicit stages.