On the Stability of the Nystrom Method for the Muskhelishvili Equation on Contours with Corners
(2013) In SIAM Journal on Numerical Analysis 51(3). p.1757-1776- Abstract
- The stability of the Nystrom method for the Muskhelishvili equation on piecewise smooth simple contours Gamma is studied. It is shown that in the space L-2 the method is stable if and only if certain operators A tau(j) from an algebra of Toeplitz operators are invertible. The operators A tau(j) depend on the parameters of the equation considered, on the opening angles theta(j) of the corner points t(j) is an element of Gamma, and on parameters of the approximation method mentioned. Numerical experiments show that there are opening angles where the operators A tau(j) are noninvertible. Therefore, for contours with such corners the method under consideration is not stable. Otherwise, the method is always stable. Numerical examples show an... (More)
- The stability of the Nystrom method for the Muskhelishvili equation on piecewise smooth simple contours Gamma is studied. It is shown that in the space L-2 the method is stable if and only if certain operators A tau(j) from an algebra of Toeplitz operators are invertible. The operators A tau(j) depend on the parameters of the equation considered, on the opening angles theta(j) of the corner points t(j) is an element of Gamma, and on parameters of the approximation method mentioned. Numerical experiments show that there are opening angles where the operators A tau(j) are noninvertible. Therefore, for contours with such corners the method under consideration is not stable. Otherwise, the method is always stable. Numerical examples show an excellent convergence of the method. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/3979401
- author
- Didenko, Victor D. and Helsing, Johan LU
- organization
- publishing date
- 2013
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Muskhelishvili equation, Nystrom method, stability
- in
- SIAM Journal on Numerical Analysis
- volume
- 51
- issue
- 3
- pages
- 1757 - 1776
- publisher
- Society for Industrial and Applied Mathematics
- external identifiers
-
- wos:000321043900017
- scopus:84884999223
- ISSN
- 0036-1429
- DOI
- 10.1137/120889472
- 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
- 6aafea7f-0d81-447b-a6b5-59e01579a9fa (old id 3979401)
- alternative location
- http://www.maths.lth.se/na/staff/helsing/VJ4.pdf
- date added to LUP
- 2016-04-01 13:25:59
- date last changed
- 2022-03-29 07:25:20
@article{6aafea7f-0d81-447b-a6b5-59e01579a9fa,
abstract = {{The stability of the Nystrom method for the Muskhelishvili equation on piecewise smooth simple contours Gamma is studied. It is shown that in the space L-2 the method is stable if and only if certain operators A tau(j) from an algebra of Toeplitz operators are invertible. The operators A tau(j) depend on the parameters of the equation considered, on the opening angles theta(j) of the corner points t(j) is an element of Gamma, and on parameters of the approximation method mentioned. Numerical experiments show that there are opening angles where the operators A tau(j) are noninvertible. Therefore, for contours with such corners the method under consideration is not stable. Otherwise, the method is always stable. Numerical examples show an excellent convergence of the method.}},
author = {{Didenko, Victor D. and Helsing, Johan}},
issn = {{0036-1429}},
keywords = {{Muskhelishvili equation; Nystrom method; stability}},
language = {{eng}},
number = {{3}},
pages = {{1757--1776}},
publisher = {{Society for Industrial and Applied Mathematics}},
series = {{SIAM Journal on Numerical Analysis}},
title = {{On the Stability of the Nystrom Method for the Muskhelishvili Equation on Contours with Corners}},
url = {{https://lup.lub.lu.se/search/files/3368173/4226460.pdf}},
doi = {{10.1137/120889472}},
volume = {{51}},
year = {{2013}},
}