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Convergence analysi...
Convergence analysis of least-squares collocation methods for nonlinear higher-index differential–algebraic equations
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- Hanke, Michael (författare)
- KTH,Numerisk analys, NA
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März, R. (författare)
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(creator_code:org_t)
- Elsevier BV, 2021
- 2021
- Engelska.
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Ingår i: Journal of Computational and Applied Mathematics. - : Elsevier BV. - 0377-0427 .- 1879-1778. ; 387
- Relaterad länk:
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https://urn.kb.se/re...
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visa fler...
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https://doi.org/10.1...
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Abstract
Ämnesord
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- 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.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Nyckelord
- 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
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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