Computing with B-series

David I. Ketcheson; Hendrik Ranocha

doi:10.1145/3573384

Computing with B-series

David I. Ketcheson, Hendrik Ranocha

Research output: Contribution to journal › Article › peer-review

3 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 language	English (US)
Journal	ACM Transactions on Mathematical Software
DOIs	https://doi.org/10.1145/3573384
State	Published - 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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10.1145/3573384

https://repository.kaust.edu.sa/bitstream/10754/673827/5/3573384.pdf

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title = "Computing with B-series",

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.",

author = "Ketcheson, {David I.} and Hendrik Ranocha",

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{\textquoteright}s Excellence Strategy EXC 2044-390685587, Mathematics M{\"u}nster: Dynamics-Geometry-Structure.",

year = "2022",

month = dec,

day = "2",

doi = "10.1145/3573384",

language = "English (US)",

journal = "ACM Transactions on Mathematical Software",

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AU - Ketcheson, David I.

AU - Ranocha, Hendrik

N1 - 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.

PY - 2022/12/2

Y1 - 2022/12/2

N2 - 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.

AB - 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.

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M3 - Article

SN - 0098-3500

JO - ACM Transactions on Mathematical Software

JF - ACM Transactions on Mathematical Software

ER -

Computing with B-series

Abstract

Bibliographical note

ASJC Scopus subject areas

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