On the random generation of Butcher trees

Abstract

The main goal of this paper is to provide an algorithm for the random sampling of Butcher trees and the probabilistic numerical solution of ordinary differential equations (ODEs). This approach complements and simplifies a recent approach to the probabilistic representation of ODE solutions, by removing the need to generate random branching times. The random sampling of trees is compared to the finite order truncation of Butcher series in numerical experiments.