Marcella Oliani: Order conditions for Runge-Kutta methods. Diplom thesis, Ferrara 1995. Original title: Condizioni d'ordine per metodi di Runge-Kutta.

RUNGE-KUTTA METHODS From Euler's method to Runge-Kutta methods Error bounds for single-step methods Order conditions for Runge-Kutta methods of height 2 Definition of Runge-Kutta methods A C++ program for Runge-Kutta methods Order conditions for Runge-Kutta methods of height 3 Order conditions for Runge-Kutta methods of height 4 BUTCHER TREES Elementary differentials associated to a tree Number of classes of rooted trees The Taylor series of the exact solution Faa' di Bruno's formula The derivatives of the numerical solution A theorem which characterizes the order of a Runge-Kutta method REFERENCES