B-series and B-series Coefficients

J. C. Butcher2
Department of Mathematics,
University of Auckland,
Auckland, New Zealand
Received February 8, 2010; accepted in revised form February 22, 2010.
Abstract: B-series, together with the algebraic system which underpins them, are essential
tools in the study of properties of numerical methods for evolutionary problems. This
paper surveys the properties of these constructs and relates the theory to applications in
numerical analysis.

c 2010 European Society of Computational Methods in Sciences and Engineering
Keywords: B-series, Runge-Kutta methods, order conditions, effective order, singlyimplicit
Mathematics Subject Classification: 65L05, 65L06


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