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Stability of the Nyström Method for the Sherman–Lauricella Equation

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Author

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.

Department/s

Publishing year

2011

Language

English

Pages

1127-1148

Publication/Series

SIAM Journal on Numerical Analysis

Volume

49

Issue

3

Document type

Journal article

Publisher

Society for Industrial and Applied Mathematics

Topic

  • Mathematics

Status

Published

Research group

  • Harmonic Analysis and Applications
  • Harmonic Analysis and Applications

ISBN/ISSN/Other

  • ISSN: 0036-1429