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Aromatic Butcher series
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.ORCID iD: 0000-0003-3699-6244
2016 (English)In: Foundations of Computational Mathematics, ISSN 1615-3375, E-ISSN 1615-3383, Vol. 16, no 1, 183-215 p.Article in journal (Refereed) Published
Abstract [en]

We show that without other further assumption than affine equivariance and locality, a numerical integrator has an expansion in a generalized form of Butcher series (B-series), which we call aromatic B-series. We obtain an explicit description of aromatic B-series in terms of elementary differentials associated to aromatic trees, which are directed graphs generalizing trees. We also define a new class of integrators, the class of aromatic Runge-Kutta methods, that extends the class of Runge-Kutta methods and have aromatic B-series expansion but are not B-series methods. Finally, those results are partially extended to the case of more general affine group equivariance.

Place, publisher, year, edition, pages
New York: Springer-Verlag New York, 2016. Vol. 16, no 1, 183-215 p.
Keyword [en]
B-Series, Butcher series, equivariance, aromatic series, aromatic trees, functional graph, directed pseudo-forest
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-99649DOI: 10.1007/s10208-015-9245-0ISI: 000371263400006OAI: oai:DiVA.org:umu-99649DiVA: diva2:787387
Available from: 2015-02-10 Created: 2015-02-10 Last updated: 2017-12-04Bibliographically approved

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