On projected Runge-Kutta methods for differential-algebraic equations (Q1176474)

The author considers projected Runge-Kutta methods for differential- algebraic equations of index 2 having the form \(y'=f(y,z)\), \(0=g(y)\). These methods have recently been introduced by \textit{U. M. Ascher} and \textit{L. R. Petzold} [SIAM J. Numer. Anal. 28, No. 4, 1097-1120 (1991; Zbl 0732.65067)]. Here it is shown that such a method can be regarded as the limiting case of a standard application of a Runge-Kutta method with an additional very small implicit Euler step. This interpretation makes it possible to transfer well known results on order and superconvergence from standard Runge-Kuta methods. The paper does not contain numerical results.