Stability of the Nyström Method for the Sherman–Lauricella Equation

Summary, in English

The stability of the Nyström method for the Sherman–Lauricella equation on piecewise smooth closed simple contour $\Gamma$ is studied. It is shown that in the space $L_2$ the method is stable if and only if certain operators associated with the corner points of $\Gamma$ are invertible. If $\Gamma$ does not have corner points, the method is always stable. Numerical experiments show the transformation of solutions when the unit circle is continuously transformed into the unit square, and then into various rhombuses. Examples also show an excellent convergence of the method.

• Författare: Victor Didenko; Johan Helsing
• Avdelning/ar: Matematik LTH; Harmonic Analysis and Applications; eSSENCE: The e-Science Collaboration
• Publiceringsår: 2011
• Språk: Engelska
• Sidor: 1127-1148
• Publikation/Tidskrift/Serie: SIAM Journal on Numerical Analysis
• Volym: 49
• Issue: 3
• Fulltext: - 719 kB; Download statistics
• Länkar: http://www.maths.lth.se/na/staff/helsing/VJ.pdf; http://dx.doi.org/10.1137/100811829
• Dokumenttyp: Artikel i tidskrift
• Förlag: Society for Industrial and Applied Mathematics
• Ämne: Mathematics
• Status: Published
• Forskningsgrupp: Harmonic Analysis and Applications; Harmonic Analysis and Applications
• ISBN/ISSN/Övrigt: ISSN: 0036-1429