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ON THE STABILITY OF THE NYSTRÖM METHOD FOR THE MUSKHELISHVILI EQUATION ON CONTOURS WITH CORNERS

DIDENKO, VICTOR D. ; HELSING, JOHAN

SIAM journal on numerical analysis, 2013-01, Vol.51 (3), p.1757-1776 [Periódico revisado por pares]

Philadelphia: Society for Industrial and Applied Mathematics

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Título:
ON THE STABILITY OF THE NYSTRÖM METHOD FOR THE MUSKHELISHVILI EQUATION ON CONTOURS WITH CORNERS
Autor: DIDENKO, VICTOR D. ; HELSING, JOHAN
Assuntos: Algebra ; Applied mathematics ; Approximation ; Contours ; Convergence ; Corners ; Differential equations ; Geometric angles ; Integral equations ; Invertibility ; Matematik ; Mathematical analysis ; Mathematical functions ; Mathematical integrals ; Mathematical models ; Mathematical problems ; Mathematical theorems ; Mathematics ; Methods ; Muskhelishvili equation ; Natural Sciences ; Naturvetenskap ; Nystrom method ; Operators ; Quotients ; Stability
É parte de: SIAM journal on numerical analysis, 2013-01, Vol.51 (3), p.1757-1776
Notas: ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
Descrição: The stability of the Nyström method for the Muskhelishvili equation on piecewise smooth simple contours Γ is studied. It is shown that in the space L² the method is stable if and only if certain operators ${A_{{T_j}}}$ from an algebra of Toeplitz operators are invertible. The operators ${A_{{T_j}}}$ depend on the parameters of the equation considered, on the opening angles θ j of the corner points T j ∈ Γ, and on parameters of the approximation method mentioned. Numerical experiments show that there are opening angles where the operators ${A_{{T_j}}}$ 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.
Editor: Philadelphia: Society for Industrial and Applied Mathematics
Idioma: Inglês

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ON THE STABILITY OF THE NYSTRÖM METHOD FOR THE MUSKHELISHVILI EQUATION ON CONTOURS WITH CORNERS

DIDENKO, VICTOR D. ; HELSING, JOHAN

Philadelphia: Society for Industrial and Applied Mathematics

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