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Order conditions for numerical integrators obtained by composing simpler integrators

A. Murua , J.M. Sanz–Serna


For numerical one–step integration methods obtained by composing or concatenating simpler methods, we study the conditions that the method has to satisfy to attain a prescribed order of accuracy. An existing methodology uses the Baker–Campbell–Hausdorff formula; we develop an alternative technique based on the use of rooted trees and similar to that which is standard in the analysis of Runge–Kutta methods. In the present approach, the order conditions can be written down easily by transcribing the structure of the corresponding rooted trees.

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