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

Abstract

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.