What are Butcher series, really?
Preprint, 2015

A review of early work in Runge-Kutta methods and Butcher (B) series, especially Robin Merson's 1957 paper and John Butcher's early work; and a discussion of work in the past decade on algebraic and geometric characterisations of Butcher series, culminating in the recent result that a method has Butcher series if and only if the methods applied to any pair of affine-related vector fields (possibly on spaces of different dimensions) are themselves affine-related.


Robert McLachlan

Klas Modin

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Hans Munthe-Kaas

Olivier Verdier

Subject Categories

Computational Mathematics



Basic sciences

More information