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 methods. Mathematics Subject Classification: 65L05, 65L06