RT info:eu-repo/semantics/bookPart
T1 Formal series and numerical integrators: some history and some new techniques
A1 Murua Uria, Ander
A1 Sanz Serna, Jesús María
AB This paper provides a brief history of B-series and the associated Butchergroup and presents the new theory of word series and extended word series. B-series(Hairer and Wanner 1976) are formal series of functions parameterized by rooted trees.They greatly simplify the study of Runge-Kutta schemes and other numerical integrators.We examine the problems that led to the introduction of B-series and survey a number ofmore recent developments, including applications outside numerical mathematics. Wordseries (series of functions parameterized by words from an alphabet) provide in somecases a very convenient alternative to B-series. Associated with word series is a group Gof coe cients with a composition rule simpler than the corresponding rule in the Butchergroup. From a more mathematical point of view, integrators, like Runge-Kutta schemes,that are a ne equivariant are represented by elements of the Butcher group, integratorsthat are equivariant with respect to arbitrary changes of variables are represented byelements of the word group G.
PB Higher Education Press
SN 978-7-04-043453-8
YR 2015
FD 2015
LK http://uvadoc.uva.es/handle/10324/28913
UL http://uvadoc.uva.es/handle/10324/28913
LA eng
NO Proceedings of the 8th International Congress on Industrial and Applied Mathematics (ICIAM 2015), Lei Guo and Zhi-Ming eds., Higher Education Press, Beijing, 2015, 311-331
DS UVaDOC
RD 01-jun-2024