Word series for dynamical systems and their numerical integrators

Murua, A.; Sanz Serna, Jesús María

dc.contributor.author	Murua, A.
dc.contributor.author	Sanz Serna, Jesús María
dc.date.accessioned	2021-04-30T09:29:08Z
dc.date.available	2021-04-30T09:29:08Z
dc.date.issued	2017-06
dc.identifier.bibliographicCitation	Murua, A. & Sanz-Serna, J. M. (2015). Word Series for Dynamical Systems and Their Numerical Integrators. Foundations of Computational Mathematics, 17(3), 675–712.
dc.identifier.issn	1615-3375
dc.identifier.uri	http://hdl.handle.net/10016/32514
dc.description.abstract	We study word series and extended word series, classes of formal series for the analysis of some dynamical systems and their discretizations. These series are similar to but more compact than B-series. They may be composed among themselves by means of a simple rule. While word series have appeared before in the literature, extended word series are introduced in this paper. We exemplify the use of extended word series by studying the reduction to normal form and averaging of some perturbed integrable problems. We also provide a detailed analysis of the behavior of splitting numerical methods for those problems.
dc.description.sponsorship	A. Murua and J.M. Sanz-Serna have been supported by Projects MTM2013-46553-C3-2-P and MTM2013-46553-C3-1-P from Ministerio de Economía y Comercio, Spain. Additionally A. Murua has been partially supported by the Basque Government (Consolidated Research Group IT649-13).
dc.format.extent	38
dc.language.iso	eng
dc.publisher	Springer Nature
dc.rights	© 2015, SFoCM.
dc.subject.other	Word series
dc.subject.other	Hopf algebras
dc.subject.other	Hamiltonian problems
dc.subject.other	Normal forms
dc.subject.other	Averaging
dc.subject.other	Splitting algorithms
dc.subject.other	Oscillatory differential-equations
dc.subject.other	Formal series
dc.subject.other	B-series
dc.subject.other	Trees
dc.title	Word series for dynamical systems and their numerical integrators
dc.type	article
dc.subject.eciencia	Matemáticas
dc.identifier.doi	https://doi.org/10.1007/s10208-015-9295-3
dc.rights.accessRights	openAccess
dc.relation.projectID	Gobierno de España. MTM2013-46553-C3-2-P
dc.relation.projectID	Gobierno de España. MTM2013-46553-C3-1-P
dc.type.version	acceptedVersion
dc.identifier.publicationfirstpage	675
dc.identifier.publicationissue	3
dc.identifier.publicationlastpage	712
dc.identifier.publicationtitle	Foundations of Computational Mathematics
dc.identifier.publicationvolume	17
dc.identifier.uxxi	AR/0000020072
dc.contributor.funder	Ministerio de Economía y Competitividad (España)