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On the Stability of the Nystrom Method for the Muskhelishvili Equation on Contours with Corners

Authors
Publisher
SIAM Publications
Publication Date
Keywords
  • Nystrom Method
  • Muskhelishvili Equation
  • Stability
  • Mathematics And Statistics
Disciplines
  • Mathematics

Abstract

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.

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