<div class="csl-bib-body">
<div class="csl-entry">Weinmüller, E., Hohenegger, M., Settanni, G., & Wolde, M. (2024, September 15). <i>Approximating singular ODEs using finite differences and collocation codes</i> [Conference Presentation]. 22nd International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2024), Kreta, Greece. http://hdl.handle.net/20.500.12708/206186</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/206186
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dc.description.abstract
Boundary value problems in ODEs with singularities arise in numerous mathematical models describing real-life phenomena in natural sciences and engineering. This motivates vivid research activities aiming to characterize the analytical properties of singular problems, to investigate convergence of the standard numerical methods when they are applied to simulate differential equation with singularities, and to provide software for their efficient numerical treatment. There are two well-known, high order numerical methods which we focus on in this paper, the finite difference schemes and the collocation methods. Those methods proved to be dependable and highly accurate in the context of regular differential equations, so the question arises how do they preform for singular problems. While, there is a strong evidence for the collocation schemes to be a robust method to solve singular systems in a stable and efficient way, finite difference schemes are still considered less suitable for this problem class.
In this paper, we shall compare the performance of the code HOFiD bvp [1] based on the high order finite difference schemes and bvpsuite2.0 [2] based on polynomial collocation, when the codes are applied to singular problems in ODEs. We are fully aware of the difficulties in a code comparison, so here, we will try to only diagnose the potential improvements, we could address in the next update of the codes.
en
dc.language.iso
en
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dc.subject
Boundary value problems
en
dc.subject
Collocation method
en
dc.subject
Finite difference scheme
en
dc.subject
Mesh adaptation
en
dc.subject
Ordinary differential equations
en
dc.subject
Singular problems
en
dc.title
Approximating singular ODEs using finite differences and collocation codes
en
dc.type
Presentation
en
dc.type
Vortrag
de
dc.contributor.affiliation
TU Wien, Austria
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dc.contributor.affiliation
TU Wien, Austria
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dc.type.category
Conference Presentation
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tuw.researchTopic.id
C4
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tuw.researchTopic.id
C5
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tuw.researchTopic.name
Mathematical and Algorithmic Foundations
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tuw.researchTopic.name
Computer Science Foundations
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tuw.researchTopic.value
50
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tuw.researchTopic.value
50
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tuw.publication.orgunit
E101 - Institut für Analysis und Scientific Computing
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tuw.author.orcid
0009-0005-6657-2364
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tuw.event.name
22nd International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2024)
en
tuw.event.startdate
11-09-2024
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tuw.event.enddate
17-09-2024
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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
Kreta
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tuw.event.country
GR
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tuw.event.presenter
Weinmüller, Ewa
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wb.sciencebranch
Mathematik
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wb.sciencebranch.oefos
1010
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wb.sciencebranch.value
100
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item.cerifentitytype
Publications
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item.languageiso639-1
en
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item.fulltext
no Fulltext
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item.openairetype
conference paper not in proceedings
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item.openairecristype
http://purl.org/coar/resource_type/c_18cp
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item.grantfulltext
none
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crisitem.author.dept
E101 - Institut für Analysis und Scientific Computing
