Webbläsaren som du använder stöds inte av denna webbplats. Alla versioner av Internet Explorer stöds inte längre, av oss eller Microsoft (läs mer här: * https://www.microsoft.com/en-us/microsoft-365/windows/end-of-ie-support).

Var god och använd en modern webbläsare för att ta del av denna webbplats, som t.ex. nyaste versioner av Edge, Chrome, Firefox eller Safari osv.

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

Publiceringsår

2011

Språk

Engelska

Sidor

403-414

Publikation/Tidskrift/Serie

East Asian Journal on Applied Mathematics

Volym

1

Issue

4

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