Features of the Nyström method for the Sherman-Lauricella equation on Piecewise Smooth Contours
(2011) In East Asian Journal on Applied Mathematics 1(4). p.403-414- Abstract
- The stability of the Nyström method for the Sherman-Lauricella equation on contours with corner points $c_j$, $j=0,1,...,m$ relies on the invertibility of certain operators $A_{c_j}$ belonging to an algebra of Toeplitz operators. The operators $A_{c_j}$ do not depend on the shape of the contour, but on the opening angle $\theta_j$ of the corresponding corner $c_j$ and on parameters of the approximation method mentioned. They have a complicated structure and there is no analytic tool to verify their invertibility. To study this problem, the original Nyström method is applied to the Sherman-Lauricella equation on a special model contour that has only one corner point with varying opening angle $\theta_j$. In the interval $(0.1\pi,1.9\pi)$,... (More)
- The stability of the Nyström method for the Sherman-Lauricella equation on contours with corner points $c_j$, $j=0,1,...,m$ relies on the invertibility of certain operators $A_{c_j}$ belonging to an algebra of Toeplitz operators. The operators $A_{c_j}$ do not depend on the shape of the contour, but on the opening angle $\theta_j$ of the corresponding corner $c_j$ and on parameters of the approximation method mentioned. They have a complicated structure and there is no analytic tool to verify their invertibility. To study this problem, the original Nyström method is applied to the Sherman-Lauricella equation on a special model contour that has only one corner point with varying opening angle $\theta_j$. In the interval $(0.1\pi,1.9\pi)$, it is found that there are $8$ values of $\theta_j$ where the invertibility of the operator $A_{c_j}$ may fail, so the corresponding original Nyström method on any contour with corner points of such magnitude cannot be stable and requires modification. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/2203901
- author
- Didenko, Victor and Helsing, Johan LU
- organization
- publishing date
- 2011
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Sherman-Lauricella equation, Nyström method, stability
- in
- East Asian Journal on Applied Mathematics
- volume
- 1
- issue
- 4
- pages
- 403 - 414
- publisher
- Global Science Press
- external identifiers
-
- wos:000208793300004
- scopus:84885899582
- ISSN
- 2079-7370
- DOI
- 10.4208/eajam.240611.070811a
- 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
- 95f9318e-3d6d-4f67-9db3-a83379e575d8 (old id 2203901)
- alternative location
- http://www.maths.lth.se/na/staff/helsing/VJ2.pdf
- date added to LUP
- 2016-04-01 10:44:22
- date last changed
- 2022-01-26 02:04:03
@article{95f9318e-3d6d-4f67-9db3-a83379e575d8,
abstract = {{The stability of the Nyström method for the Sherman-Lauricella equation on contours with corner points $c_j$, $j=0,1,...,m$ relies on the invertibility of certain operators $A_{c_j}$ belonging to an algebra of Toeplitz operators. The operators $A_{c_j}$ do not depend on the shape of the contour, but on the opening angle $\theta_j$ of the corresponding corner $c_j$ and on parameters of the approximation method mentioned. They have a complicated structure and there is no analytic tool to verify their invertibility. To study this problem, the original Nyström method is applied to the Sherman-Lauricella equation on a special model contour that has only one corner point with varying opening angle $\theta_j$. In the interval $(0.1\pi,1.9\pi)$, it is found that there are $8$ values of $\theta_j$ where the invertibility of the operator $A_{c_j}$ may fail, so the corresponding original Nyström method on any contour with corner points of such magnitude cannot be stable and requires modification.}},
author = {{Didenko, Victor and Helsing, Johan}},
issn = {{2079-7370}},
keywords = {{Sherman-Lauricella equation; Nyström method; stability}},
language = {{eng}},
number = {{4}},
pages = {{403--414}},
publisher = {{Global Science Press}},
series = {{East Asian Journal on Applied Mathematics}},
title = {{Features of the Nyström method for the Sherman-Lauricella equation on Piecewise Smooth Contours}},
url = {{https://lup.lub.lu.se/search/files/2094819/4226461.pdf}},
doi = {{10.4208/eajam.240611.070811a}},
volume = {{1}},
year = {{2011}},
}