Description
Why trees in Runge-Kutta methods
While Runge-Kutta methods for solving ODE have been introduced around 1900, J. Butcher presented in the 1970's a set of algebraic techniques to check the order of a Runge-Kutta method.
This approach in now one of the pillars of the geometric integration theory. We give an intuitive account on why trees appear in such a problem and how transform is into an algebraic problem. From a joint work with Lorenzi Agabiti and Lorenzo Zambotti (LPSM, Paris).