  Runge-Kutta methods have an irreplaceable position among numerical methods
designed to solve ordinary differential equations. Especially, implicit ones
are suitable for approximating solutions of stiff initial value problems. We
propose a new way of deriving coefficients of implicit Runge-Kutta methods.
This approach based on repeated integrals yields both new and well-known
Butcher's tableaux. We discuss the properties of newly derived methods and
compare them with standard collocation implicit Runge-Kutta methods in a series
of numerical experiments. In particular, we observe higher accuracy and higher
experimental order of convergence of some newly derived methods.
