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A reliable direct numerical treatment of differential–algebraic equations by overdetermined collocation: An operator approach
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.ORCID iD: 0000-0003-4950-6646
2021 (English)In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 387, article id 112520Article in journal (Refereed) Published
Abstract [en]

Recently reported experiments and theoretical contributions concerning overdetermined polynomial collocation applied to higher-index differential–algebraic equations give rise to the conjecture that next to the existing derivative-array based methods there is further potential toward a reliable direct numerical treatment of DAEs. By analyzing first-order differential–algebraic operators and their special approximations in detail, we contribute to justify the overdetermined polynomial collocation applied to first-order higher-index differential–algebraic equations and fill the hitherto existing gap between the theoretical convergence results and its practical realization. Moreover, we shortly touch related questions for higher-order DAEs. We discuss several practical aspects of higher-order differential–algebraic operators and the associated equations which may be important for the application of collocation methods.

Place, publisher, year, edition, pages
Elsevier BV , 2021. Vol. 387, article id 112520
Keywords [en]
Differential–algebraic operator, Essentially ill-posed problem, Higher index, Higher-order differential–algebraic equation, Least-squares problem, Overdetermined polynomial collocation, Differential equations, Polynomials, Algebraic equations, Ill posed problem, Least squares problems, Polynomial collocation, Numerical methods
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-268617DOI: 10.1016/j.cam.2019.112520ISI: 000614702800027Scopus ID: 2-s2.0-85072782048OAI: oai:DiVA.org:kth-268617DiVA, id: diva2:1426975
Note

QC 20200428

Available from: 2020-04-28 Created: 2020-04-28 Last updated: 2022-06-26Bibliographically approved

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Hanke, Michael

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  • de-DE
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