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.

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