<div class="csl-bib-body">
<div class="csl-entry">Auzinger, W., Koch, O., & Quell, M. (2017). Adaptive high-order splitting methods for systems of nonlinear evolution equations with periodic boundary conditions. <i>Numerical Algorithms</i>. https://doi.org/10.1007/s11075-016-0206-8</div>
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We assess the applicability and efficiency of time-adaptive high-order splitting methods applied for the numerical solution of (systems of) nonlinear parabolic problems under periodic boundary conditions. We discuss in particular several applications generating intricate patterns and displaying nonsmooth solution dynamics. First, we give a general error analysis for splitting methods for parabolic problems under periodic boundary conditions and derive the necessary smoothness requirements on the exact solution in particular for the Gray–Scott equation and the Van der Pol equation. Numerical examples demonstrate the convergence of the methods and serve to compare the efficiency of different time-adaptive splitting schemes and of splitting into either two or three operators, based on appropriately constructed a posteriori local error estimators.
en
dc.language
English
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dc.language.iso
en
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dc.publisher
Springer
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dc.relation.ispartof
Numerical Algorithms
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dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
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dc.subject
Nonlinear evolution equations
en
dc.subject
Splitting methods
en
dc.subject
Adaptive time integration
en
dc.subject
Local error
en
dc.subject
Convergence
en
dc.title
Adaptive high-order splitting methods for systems of nonlinear evolution equations with periodic boundary conditions
en
dc.type
Article
en
dc.type
Artikel
de
dc.rights.license
Creative Commons Namensnennung 4.0 International
de
dc.rights.license
Creative Commons Attribution 4.0 International
en
dcterms.dateSubmitted
2015-12-23
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dc.rights.holder
The Author(s) 2016
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dc.type.category
Original Research Article
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tuw.journal.peerreviewed
true
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tuw.peerreviewed
true
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tuw.version
vor
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dcterms.isPartOf.title
Numerical Algorithms
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tuw.publication.orgunit
E101 - Institut für Analysis und Scientific Computing
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tuw.publisher.doi
10.1007/s11075-016-0206-8
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dc.date.onlinefirst
2016-10-04
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dc.identifier.eissn
1572-9265
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dc.identifier.libraryid
AC11361245
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dc.identifier.urn
urn:nbn:at:at-ubtuw:3-2830
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tuw.author.orcid
0000-0002-9631-2601
-
tuw.author.orcid
0000-0002-1956-221X
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tuw.author.orcid
0000-0002-4787-152X
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dc.rights.identifier
CC BY 4.0
de
dc.rights.identifier
CC BY 4.0
en
wb.sci
true
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item.languageiso639-1
en
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item.openairetype
research article
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open
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with Fulltext
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Publications
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item.openairecristype
http://purl.org/coar/resource_type/c_2df8fbb1
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item.openaccessfulltext
Open Access
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crisitem.author.dept
E101 - Institut für Analysis und Scientific Computing
-
crisitem.author.dept
E101 - Institut für Analysis und Scientific Computing