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Stability of the Nyström Method for the Sherman–Lauricella Equation

Didenko, Victor and Helsing, Johan LU (2011) In SIAM Journal on Numerical Analysis 49(3). p.1127-1148
Abstract
The stability of the Nyström method for the Sherman–Lauricella equation on piecewise smooth closed simple contour $\Gamma$ is studied. It is shown that in the space $L_2$ the method is stable if and only if certain operators associated with the corner points of $\Gamma$ are invertible. If $\Gamma$ does not have corner points, the method is always stable. Numerical experiments show the transformation of solutions when the unit circle is continuously transformed into the unit square, and then into various rhombuses. Examples also show an excellent convergence of the method.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
SIAM Journal on Numerical Analysis
volume
49
issue
3
pages
1127 - 1148
publisher
SIAM Publications
external identifiers
  • wos:000292033100011
  • scopus:79960426076
ISSN
0036-1429
DOI
10.1137/100811829
language
English
LU publication?
yes
id
c014ed13-8f2e-4329-9cd1-c619b1053427 (old id 1977417)
alternative location
http://www.maths.lth.se/na/staff/helsing/VJ.pdf
date added to LUP
2011-08-23 13:50:19
date last changed
2017-05-21 03:19:26
@article{c014ed13-8f2e-4329-9cd1-c619b1053427,
  abstract     = {The stability of the Nyström method for the Sherman–Lauricella equation on piecewise smooth closed simple contour $\Gamma$ is studied. It is shown that in the space $L_2$ the method is stable if and only if certain operators associated with the corner points of $\Gamma$ are invertible. If $\Gamma$ does not have corner points, the method is always stable. Numerical experiments show the transformation of solutions when the unit circle is continuously transformed into the unit square, and then into various rhombuses. Examples also show an excellent convergence of the method.},
  author       = {Didenko, Victor and Helsing, Johan},
  issn         = {0036-1429},
  language     = {eng},
  number       = {3},
  pages        = {1127--1148},
  publisher    = {SIAM Publications},
  series       = {SIAM Journal on Numerical Analysis},
  title        = {Stability of the Nyström Method for the Sherman–Lauricella Equation},
  url          = {http://dx.doi.org/10.1137/100811829},
  volume       = {49},
  year         = {2011},
}