Setup of Order Conditions for Splitting Methods

For operator splitting methods, an approach based on Taylor expansion and the particular structure of its leading term as an element of a free Lie algebra is used for the setup of a system of order conditions. Along with a brief review of the underlying theoretical background, we discuss the implementation of the resulting algorithm in computer algebra, in particular using Maple 18 (Maple is a trademark of MapleSoft\(^\mathrm{TM}\).). A parallel version of such a code is described, and its performance on a computational node with 16 threads is documented.

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