Computing with B-series

David I. Ketcheson, Hendrik Ranocha

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We present BSeries.jl, a Julia package for the computation and manipulation of B-series, which are a versatile theoretical tool for understanding and designing discretizations of differential equations. We give a short introduction to the theory of B-series and associated concepts and provide examples of their use, including method composition and backward error analysis. The associated software is highly performant and makes it possible to work with B-series of high order.
Original languageEnglish (US)
JournalACM Transactions on Mathematical Software
DOIs
StatePublished - Dec 2 2022

Bibliographical note

KAUST Repository Item: Exported on 2022-12-06
Acknowledgements: We are grateful to Prof. Ernst Hairer for helpful discussions related to the example in Section 2.6 and for pointing out the closed formula for g(z) in (37). The first author was supported by the King Abdullah University of Science and Technology (KAUST). The second author was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2044-390685587, Mathematics Münster: Dynamics-Geometry-Structure.

ASJC Scopus subject areas

  • Software
  • Applied Mathematics

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