Order conditions for two-step Runge-Kutta methods (Q1360556)

Recently \textit{Z. Jackiewicz} and \textit{S. Tracogna} [SIAM J. Numer. Anal. 32, No. 5, 1390-1427 (1995; Zbl 0837.65074)] derived order conditions for a class of two-step Runge-Kutta methods using P.\ Albrecht's linear approach. Later, Wanner and Hairer obtained the order conditions using the theory of B-series. In the present paper these conditions are derived with the aid of algebraic criteria introduced by \textit{J. C. Butcher} in his book [The numerical analysis of ordinary differential equations. Runge-Kutta and general linear methods (1987; Zbl 0616.65072)] in the context of general linear methods. Also a Mathematica program is presented that generates the order conditions.