Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes

Handle URI:
http://hdl.handle.net/10754/617789
Title:
Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes
Authors:
Auzinger, Winfried; Hofstätter, Harald; Ketcheson, David I. ( 0000-0002-1212-126X ) ; Koch, Othmar
Abstract:
We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular schemes are constructed via setup and solution of polynomial systems for the splitting coefficients. To this end we use and modify a recent approach for generating these systems for a large class of splittings. In particular, various types of pairs of schemes intended for use in adaptive integrators are constructed.
KAUST Department:
Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
Citation:
Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes 2016 BIT Numerical Mathematics
Publisher:
Springer Nature
Journal:
BIT Numerical Mathematics
Issue Date:
28-Jul-2016
DOI:
10.1007/s10543-016-0626-9
Type:
Article
ISSN:
0006-3835; 1572-9125
Sponsors:
Open access funding provided by Technische Universität Wien. This work was supported by the Austrian Science Fund (FWF) under Grant P24157-N13, and by the Vienna Science and Technology Fund (WWTF) under Grant MA-14-002. The computational results presented have been achieved in part using the Vienna Scientific Cluster (VSC).
Additional Links:
http://link.springer.com/10.1007/s10543-016-0626-9
Appears in Collections:
Articles

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DC FieldValue Language
dc.contributor.authorAuzinger, Winfrieden
dc.contributor.authorHofstätter, Haralden
dc.contributor.authorKetcheson, David I.en
dc.contributor.authorKoch, Othmaren
dc.date.accessioned2016-08-01T10:49:31Z-
dc.date.available2016-08-01T10:49:31Z-
dc.date.issued2016-07-28-
dc.identifier.citationPractical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes 2016 BIT Numerical Mathematicsen
dc.identifier.issn0006-3835-
dc.identifier.issn1572-9125-
dc.identifier.doi10.1007/s10543-016-0626-9-
dc.identifier.urihttp://hdl.handle.net/10754/617789-
dc.description.abstractWe present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular schemes are constructed via setup and solution of polynomial systems for the splitting coefficients. To this end we use and modify a recent approach for generating these systems for a large class of splittings. In particular, various types of pairs of schemes intended for use in adaptive integrators are constructed.en
dc.description.sponsorshipOpen access funding provided by Technische Universität Wien. This work was supported by the Austrian Science Fund (FWF) under Grant P24157-N13, and by the Vienna Science and Technology Fund (WWTF) under Grant MA-14-002. The computational results presented have been achieved in part using the Vienna Scientific Cluster (VSC).en
dc.language.isoenen
dc.publisherSpringer Natureen
dc.relation.urlhttp://link.springer.com/10.1007/s10543-016-0626-9en
dc.rightsThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.en
dc.subjectEvolution equationsen
dc.subjectSplitting methodsen
dc.subjectFree Lie algebraen
dc.subjectOrder conditionsen
dc.subjectLocal erroren
dc.subjectEmbedded methodsen
dc.titlePractical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemesen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Science and Engineering (CEMSE) Divisionen
dc.identifier.journalBIT Numerical Mathematicsen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionInstitut für Analysis und Scientific Computing, Technische Universität Wien, Wiedner Hauptstrasse 8-10/E101, 1040 Wien, Austriaen
dc.contributor.institutionFakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090 Wien, Austriaen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorKetcheson, Daviden
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