Subquadrature expansions for TSRK methods. There are several ways to derive convergent two-step Runge-Kutta (TSRK) methods. In this paper, the authors investigate B-series to derive the necessary order conditions up to an order six and higher as polynomials of quadratures and subquadrature expressions. Additionally, the authors compute expressions for the error coefficients of a given method up to order six. In the paper, only Runge-Kutta methods are covered, but the approach can also be extended to other classes of integrators. In addition to the theoretical findings, the authors provide and explain a MAPLE code to generate forms of the derived order conditions and the error coefficients. Hence, this MAPLE code could be used to compare different Runge-Kuttas methods. (netlib numeralgo na32)

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  1. Kværnø, Anne; Verner, J.H.: Subquadrature expansions for TSRK methods (2012)