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Logarithmic norms and nonlinear DAE stability

Higueras, I and Söderlind, Gustaf LU (2002) In BIT Numerical Mathematics 42(4). p.823-841
Abstract
Logarithmic norms are often used to estimate stability and perturbation bounds in linear ODEs. Extensions to other classes of problems such as nonlinear dynamics, DAEs and PDEs require careful modifications of the logarithmic norm. With a conceptual focus, we combine the extension to nonlinear ODEs [15] with that of matrix pencils [10] in order to treat nonlinear DAEs with a view to cover certain unbounded operators, i.e. partial differential algebraic equations. Perturbation bounds are obtained from differential inequalities for any given norm by using the relation between Dini derivatives and semi-inner products. Simple discretizations are also considered.
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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
monotonicity, nonlinear stability, error bounds, differential inequalities, differential-algebraic equations, logarithmic Lipschitz constant, logarithmic norm, difference inequalities
in
BIT Numerical Mathematics
volume
42
issue
4
pages
823 - 841
publisher
Springer
external identifiers
  • wos:000180225500008
  • scopus:0042234296
ISSN
0006-3835
DOI
10.1023/A:1021956621531
language
English
LU publication?
yes
additional info
The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Numerical Analysis (011015004)
id
dcd61de5-9ad3-40d3-957d-bd02b00b1d2d (old id 320484)
date added to LUP
2016-04-01 16:45:03
date last changed
2022-01-28 21:50:31
@article{dcd61de5-9ad3-40d3-957d-bd02b00b1d2d,
  abstract     = {{Logarithmic norms are often used to estimate stability and perturbation bounds in linear ODEs. Extensions to other classes of problems such as nonlinear dynamics, DAEs and PDEs require careful modifications of the logarithmic norm. With a conceptual focus, we combine the extension to nonlinear ODEs [15] with that of matrix pencils [10] in order to treat nonlinear DAEs with a view to cover certain unbounded operators, i.e. partial differential algebraic equations. Perturbation bounds are obtained from differential inequalities for any given norm by using the relation between Dini derivatives and semi-inner products. Simple discretizations are also considered.}},
  author       = {{Higueras, I and Söderlind, Gustaf}},
  issn         = {{0006-3835}},
  keywords     = {{monotonicity; nonlinear stability; error bounds; differential inequalities; differential-algebraic equations; logarithmic Lipschitz constant; logarithmic norm; difference inequalities}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{823--841}},
  publisher    = {{Springer}},
  series       = {{BIT Numerical Mathematics}},
  title        = {{Logarithmic norms and nonlinear DAE stability}},
  url          = {{http://dx.doi.org/10.1023/A:1021956621531}},
  doi          = {{10.1023/A:1021956621531}},
  volume       = {{42}},
  year         = {{2002}},
}