Setup of Order Conditions for Splitting Methods

  • Winfried Auzinger
  • Wolfgang Herfort
  • Harald Hofstätter
  • Othmar Koch
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9890)


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.


Evolution equations Splitting methods Order conditions Local error Taylor expansion Parallel processing 



This work was supported by the Austrian Science Fund (FWF) under grant P24157-N13, and by the Vienna Science and Technology Fund (WWTF) under grant MA-14-002. Computational results based on the ideas in this work have been achieved in part using the Vienna Scientific Cluster (VSC).


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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Winfried Auzinger
    • 1
  • Wolfgang Herfort
    • 1
  • Harald Hofstätter
    • 1
  • Othmar Koch
    • 2
  1. 1.Technische Universität WienViennaAustria
  2. 2.Universität WienViennaAustria

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