In this paper, we propose a functional fitting s-stage Runge-Kutta method which is based on the exact integration of the set of the linearly independent functions u_i(t), (i = 1, ..., s). The method is exact when the solution of the ODE can be expressed as the linear combination of u_i(t), although the method has an error for general ODE. In this work we investigate the order of accuracy of the method for general ODEs, and show that the order of accuracy of the method is at least s, if the functions u_i(t) are sufficiently smooth and the method is non-confluent. Furthermore, it is shown that the attainable order of the method is 2s, like the conventional Runge-Kutta method. An embedded pair of the Runge-Kutta methods of this type is also developed.

MINISIMPOSIUM SESSION: 6. Novel methods for ODEs