Runge-Kutta methods, trees, and Mathematica

Details Runge-Kutta methods, trees, and Mathematica Runge-Kutta methods, trees, and Mathematica

2002-11-04

arxiv.org/abs/math/0211049v1

Mathematics

Numerical Analysis

9 pages, source files include a Mathematica notebook

Scientific paper

A simple and elementary proof of Butcher's theorem on the order conditions of Runge-Kutta methods is presented. It is based on a recursive definition of rooted trees and avoids combinatorial tools such as labelings and Faa di Bruno's formula. This strictly recursive approach can easily and elegantly be implemented using modern computer algrebra systems like Mathematica. The full but short source code is included and applied to some instructive examples.

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