Setup of order conditions for splitting methods

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Abstract

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™.). 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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Auzinger, W., Herfort, W., Hofstätter, H., & Koch, O. (2016). Setup of order conditions for splitting methods. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9890 LNCS, pp. 30–42). Springer Verlag. https://doi.org/10.1007/978-3-319-45641-6_3

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