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What are Butcher series, really?

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Authors Robert McLachlan
Klas Modin
Hans Munthe-Kaas
Olivier Verdier
Publication year 2015
Published at Department of Mathematical Sciences, Mathematics
Language en
Links arxiv.org/abs/1512.00906
arxiv.org/pdf/1512.00906v1
Subject categories Computational Mathematics, Geometry

Abstract

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.

Page Manager: Webmaster|Last update: 9/11/2012
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