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Least-squares collocation for linear higher-index differential–algebraic equations
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.ORCID iD: 0000-0003-4950-6646
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2017 (English)In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 317, p. 403-431Article in journal (Refereed) Published
Abstract [en]

Differential–algebraic equations with higher index give rise to essentially ill-posed problems. Therefore, their numerical approximation requires special care. In the present paper, we state the notion of ill-posedness for linear differential–algebraic equations more precisely. Based on this property, we construct a regularization procedure using a least-squares collocation approach by discretizing the pre-image space. Numerical experiments show that the resulting method has excellent convergence properties and is not much more computationally expensive than standard collocation methods used in the numerical solution of ordinary differential equations or index-1 differential–algebraic equations. Convergence is shown for a limited class of linear higher-index differential–algebraic equations.

Place, publisher, year, edition, pages
Elsevier, 2017. Vol. 317, p. 403-431
Keywords [en]
Boundary value problem, Collocation, Differential–algebraic equation, Essentially ill-posed problem, Higher index, Initial value problem
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-200845DOI: 10.1016/j.cam.2016.12.017Scopus ID: 2-s2.0-85007586422OAI: oai:DiVA.org:kth-200845DiVA, id: diva2:1072033
Note

QC 20170207

Available from: 2017-02-07 Created: 2017-02-03 Last updated: 2017-11-29Bibliographically approved

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