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Least-Squares Collocation for Higher-Index Linear Differential-Algebraic Equations: Estimating the Instability Threshold
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.ORCID iD: 0000-0003-4950-6646
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2019 (English)In: Mathematics of Computation, ISSN 0025-5718, E-ISSN 1088-6842, Vol. 88, no 318, p. 1647-1683Article in journal (Refereed) Published
Abstract [en]

Differential-algebraic equations with higher-index give rise to essentially ill-posed problems. The overdetermined least-squares collocation for differential-algebraic equations which has been proposed recently is not much more computationally expensive than standard collocation methods for ordinary differential equations. This approach has displayed impressive convergence properties in numerical experiments, however, theoretically, till now convergence could be established merely for regular linear differential-algebraic equations with constant coefficients. We present now an estimate of the instability threshold which serves as the basic key for proving convergence for general regular linear differential-algebraic equations.

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2019. Vol. 88, no 318, p. 1647-1683
Keywords [en]
Differential-algebraic equation, higher-index, essentially ill-posed problem, collocation, boundary value problem, initial value problem
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-248306DOI: 10.1090/mcom/3393ISI: 000461927500006Scopus ID: 2-s2.0-85063938173OAI: oai:DiVA.org:kth-248306DiVA, id: diva2:1303336
Note

QC 20190409

Available from: 2019-04-09 Created: 2019-04-09 Last updated: 2020-03-05Bibliographically approved

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Hanke, Michael

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