Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Convergence analysis of least-squares collocation methods for nonlinear higher-index differential–algebraic equations
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.ORCID iD: 0000-0003-4950-6646
2019 (English)In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, article id 112514Article in journal (Refereed) Published
Abstract [en]

We approach a direct numerical treatment of nonlinear higher-index differential–algebraic equations by means of overdetermined polynomial least-squares collocation. The procedure is not much more computationally expensive than standard collocation methods for regular ordinary differential equations and the numerical experiments show promising results. Nevertheless, the theoretical basic concept turns out to be considerably challenging. So far, quite recently, convergence proofs have been published for linear problems. In the present paper we come up with a first basic qualitative convergence result for nonlinear problems.

Place, publisher, year, edition, pages
Elsevier B.V. , 2019. article id 112514
Keywords [en]
Differential–algebraic equation, Essentially ill-posed problem, Higher-index, Least-squares problem, Nonlinear problem, Polynomial collocation, Least squares approximations, Nonlinear equations, Numerical methods, Ordinary differential equations, Algebraic equations, Higher index, Ill posed problem, Least squares problems, Nonlinear problems, Algebra
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-268515DOI: 10.1016/j.cam.2019.112514Scopus ID: 2-s2.0-85072770587OAI: oai:DiVA.org:kth-268515DiVA, id: diva2:1413946
Note

QC 20200311

Available from: 2020-03-11 Created: 2020-03-11 Last updated: 2020-05-11Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full textScopus

Authority records BETA

Hanke, Michael

Search in DiVA

By author/editor
Hanke, Michael
By organisation
Numerical Analysis, NA
In the same journal
Journal of Computational and Applied Mathematics
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf