<div class="csl-bib-body">
<div class="csl-entry">Auzinger, W., Koch, O., & Weinmüller, E. (2007). <i>Numerical solution of singular boundary value problems in ordinary differential equations</i> (p. 227). http://hdl.handle.net/20.500.12708/118212</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/118212
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dc.description.abstract
We consider analytical properties and the numerical treatment of boundary value problems in ordinary differential equations with a time singularity. First, well-posedness and smoothness of the solution is discussed for the analytical problem. Subsequently, we describe the numerical treatment by collocation methods. After giving a convergence result, we introduce and analyze a new estimate for the global discretization error based on the defect correction principle. These components are the basis of successful software for singular boundary value problems developed by our group. This additionally features adaptive mesh selection by equidistribution of the global error and can also be successfully applied to solve differential algebraic equations, implicit problems, and problems with known or unknown parameters. The success of our solution approach is illustrated by virtue of examples including the computation of self-similar blow-up solutions of nonlinear PDEs and the density profile equation in hydrodynamics.
en
dc.language.iso
en
-
dc.subject
Applied Mathematics
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dc.subject
analysis
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dc.subject
Computational Mathematics
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dc.subject
Singular boundary value problems
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dc.subject
numerical methods
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dc.title
Numerical solution of singular boundary value problems in ordinary differential equations
en
dc.type
Präsentation
de
dc.type
Presentation
en
dc.description.endpage
227
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dc.type.category
Conference Presentation
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tuw.peerreviewed
false
-
tuw.publication.invited
invited
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tuw.project.title
Programm zur Lösung singulärer Randwert/
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tuw.publication.orgunit
E101-02 - Forschungsbereich Numerik
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dc.description.numberOfPages
15
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tuw.event.name
Österreichisch-Mongolischer Mathematikertag
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tuw.event.startdate
01-10-2007
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tuw.event.enddate
02-10-2007
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tuw.event.online
On Site
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tuw.event.type
Event for scientific audience
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tuw.event.place
TU Wien
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tuw.event.country
AT
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tuw.event.presenter
Koch, O.
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tuw.exhibition.type
Solo Exhibition
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wb.sciencebranch
Mathematik, Informatik
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wb.sciencebranch
Physik, Mechanik, Astronomie
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wb.sciencebranch.oefos
11
-
wb.sciencebranch.oefos
12
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wb.facultyfocus
Analysis und Scientific Computing
de
wb.facultyfocus
Analysis and Scientific Computing
en
wb.facultyfocus.faculty
E100
-
item.openairetype
Präsentation
-
item.openairetype
Presentation
-
item.openairecristype
http://purl.org/coar/resource_type/c_18cf
-
item.openairecristype
http://purl.org/coar/resource_type/c_18cf
-
item.languageiso639-1
en
-
item.cerifentitytype
Publications
-
item.cerifentitytype
Publications
-
item.fulltext
no Fulltext
-
item.grantfulltext
none
-
crisitem.author.dept
E101 - Institut für Analysis und Scientific Computing
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crisitem.author.dept
E101 - Institut für Analysis und Scientific Computing
-
crisitem.author.dept
E101 - Institut für Analysis und Scientific Computing
-
crisitem.author.orcid
0000-0002-9631-2601
-
crisitem.author.parentorg
E100 - Fakultät für Mathematik und Geoinformation
-
crisitem.author.parentorg
E100 - Fakultät für Mathematik und Geoinformation
-
crisitem.author.parentorg
E100 - Fakultät für Mathematik und Geoinformation
-
crisitem.project.funder
Fonds zur Förderung der wissenschaftlichen Forschung (FWF)