Features of the Nyström method for the ShermanLauricella equation on Piecewise Smooth Contours
(2011) In East Asian Journal on Applied Mathematics 1(4). p.403414 Abstract
 The stability of the Nyström method for the ShermanLauricella 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 ShermanLauricella 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 ShermanLauricella 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 ShermanLauricella 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:
http://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
 ShermanLauricella 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
 20797370
 DOI
 10.4208/eajam.240611.070811a
 language
 English
 LU publication?
 yes
 id
 95f9318e3d6d4f679db3a83379e575d8 (old id 2203901)
 alternative location
 http://www.maths.lth.se/na/staff/helsing/VJ2.pdf
 date added to LUP
 20111228 16:51:47
 date last changed
 20180107 04:20:57
@article{95f9318e3d6d4f679db3a83379e575d8, abstract = {The stability of the Nyström method for the ShermanLauricella 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 ShermanLauricella 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 = {20797370}, keyword = {ShermanLauricella equation,Nyström method,stability}, language = {eng}, number = {4}, pages = {403414}, publisher = {Global Science Press}, series = {East Asian Journal on Applied Mathematics}, title = {Features of the Nyström method for the ShermanLauricella equation on Piecewise Smooth Contours}, url = {http://dx.doi.org/10.4208/eajam.240611.070811a}, volume = {1}, year = {2011}, }