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