Â鶹Éçmadou

Abstract

In the last 130 years, since the first Runge-Kutta methods were discovered, the available methods of this type for numerically solving initial value problems, have increased in accuracy, efficiency and breadth of application. Furthermore, there is now a deep theoretical understanding of differential equation integrators in general, and Runge-Kutta methods in particular, involving combinatorics, trees and B-series.