On the Stability of the Nystrom Method for the Muskhelishvili Equation on Contours with Corners
Author
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.
Department/s
- Mathematics (Faculty of Engineering)
- Harmonic Analysis and Applications
- eSSENCE: The e-Science Collaboration
Publishing year
2013
Language
English
Pages
1757-1776
Publication/Series
SIAM Journal on Numerical Analysis
Volume
51
Issue
3
Full text
- Available as PDF - 560 kB
- Download statistics
Links
Document type
Journal article
Publisher
Society for Industrial and Applied Mathematics
Topic
- Mathematics
Keywords
- Muskhelishvili equation
- Nystrom method
- stability
Status
Published
Research group
- Harmonic Analysis and Applications
- Harmonic Analysis and Applications
ISBN/ISSN/Other
- ISSN: 0036-1429