Features of the Nyström method for the Sherman-Lauricella equation on Piecewise Smooth Contours
Författare
Summary, in English
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.
Avdelning/ar
- Matematik LTH
- Harmonic Analysis and Applications
- eSSENCE: The e-Science Collaboration
Publiceringsår
2011
Språk
Engelska
Sidor
403-414
Publikation/Tidskrift/Serie
East Asian Journal on Applied Mathematics
Volym
1
Issue
4
Fulltext
- Available as PDF - 307 kB
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Länkar
Dokumenttyp
Artikel i tidskrift
Förlag
Global Science Press
Ämne
- Mathematics
Nyckelord
- Sherman-Lauricella equation
- Nyström method
- stability
Status
Published
Forskningsgrupp
- Harmonic Analysis and Applications
- Harmonic Analysis and Applications
ISBN/ISSN/Övrigt
- ISSN: 2079-7370