Abstract
In this chapter we present a compact theory of the order conditions of the methods presented in Chap. II, in particular Runge–Kutta methods, partitioned Runge–Kutta methods, and composition methods by using the notion of rooted trees and B-series. These ideas lead to algebraic structures which have recently found interesting applications in quantum field theory. The chapter terminates with the Baker- Campbell-Hausdorff formula, which allows another access to the order properties of composition and splitting methods.
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© 2006 Springer
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Hairer, E., Wanner, G., Lubich, C. (2006). Order Conditions, Trees and B-Series. In: Geometric Numerical Integration. Springer Series in Computational Mathematics, vol 31 . Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-30666-8_3
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DOI: https://doi.org/10.1007/3-540-30666-8_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30663-4
Online ISBN: 978-3-540-30666-5
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