On the Stability of the Nystrom Method for the Muskhelishvili Equation on Contours with Corners
Författare
Summary, in English
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.
Avdelning/ar
- Matematik LTH
- Harmonic Analysis and Applications
- eSSENCE: The e-Science Collaboration
Publiceringsår
2013
Språk
Engelska
Sidor
1757-1776
Publikation/Tidskrift/Serie
SIAM Journal on Numerical Analysis
Volym
51
Issue
3
Fulltext
- Available as PDF - 560 kB
- Download statistics
Länkar
Dokumenttyp
Artikel i tidskrift
Förlag
Society for Industrial and Applied Mathematics
Ämne
- Mathematics
Nyckelord
- Muskhelishvili equation
- Nystrom method
- stability
Status
Published
Forskningsgrupp
- Harmonic Analysis and Applications
- Harmonic Analysis and Applications
ISBN/ISSN/Övrigt
- ISSN: 0036-1429