Stability of the Nyström Method for the Sherman–Lauricella Equation
(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:
https://lup.lub.lu.se/record/1977417
- author
- Didenko, Victor and Helsing, Johan LU
- organization
- publishing date
- 2011
- type
- Contribution to journal
- publication status
- published
- subject
- in
- SIAM Journal on Numerical Analysis
- volume
- 49
- issue
- 3
- pages
- 1127 - 1148
- publisher
- Society for Industrial and Applied Mathematics
- external identifiers
-
- wos:000292033100011
- scopus:79960426076
- ISSN
- 0036-1429
- DOI
- 10.1137/100811829
- 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
- c014ed13-8f2e-4329-9cd1-c619b1053427 (old id 1977417)
- alternative location
- http://www.maths.lth.se/na/staff/helsing/VJ.pdf
- date added to LUP
- 2016-04-01 10:48:22
- date last changed
- 2022-01-26 02:38:16
@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 = {{Society for Industrial and Applied Mathematics}}, series = {{SIAM Journal on Numerical Analysis}}, title = {{Stability of the Nyström Method for the Sherman–Lauricella Equation}}, url = {{https://lup.lub.lu.se/search/files/2150261/3878570.pdf}}, doi = {{10.1137/100811829}}, volume = {{49}}, year = {{2011}}, }