On the stability of some operator sequences and the approximate solution of singular integral equations with conjugation
type: Item
instance of: scholarly article
title: On the stability of some operator sequences and the approximate solution of singular integral equations with conjugation
zbMATH Open document ID: 0787.47035
DOI: 10.1007/BF01358954
published in: Integral Equations and Operator Theory
publication date: 1993-06-29T00:00:00Z
review text: The authors study the spline Galerkin and spline collocation method for singular integral equations of the form \[ \begin{multlined} a(t)x(t)+ {b(t)\over\pi i}\int_ \Gamma {x(\tau)\over \tau-t} d\tau+ c(t)\overline{x(t)}+ {d(t)\over \pi i}\int_ \Gamma {\overline{x(\tau)}\over \tau-t} d\tau+\\ +\int_ \Gamma h_ 1(t,\tau)x(\tau)d\tau+ \int_ \Gamma h_ 2(t,\tau)\overline{x(\tau)}d\tau= f(t),\quad t\in\Gamma,\end{multlined} \] where \(\Gamma\) is a simple, smooth and closed curve on the plane.
reviewed by: Vladimir V. Peller
Mathematics Subject Classification ID: 47G10
Mathematics Subject Classification ID: 47A50
Mathematics Subject Classification ID: 65J10
zbMATH DE Number: 222165
zbMATH Keywords: spline Galerkin method
zbMATH Keywords: spline collocation method
zbMATH Keywords: singular integral equations
author: Victor D. Didenko
author: B. Silbermann
MaRDI profile type: Publication
cites work: On the Asymptotic Convergence of Collocation Methods
cites work: Q3823775
cites work: SPLINE APPROXIMATION OF SINGULAR INTEGRAL EQUATIONS
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cites work: On spline collocation methods for boundary integral equations in the plane
cites work: A quadrature-based approach to improving the collocation method
cites work: A quadrature-based approach to improving the collocation method for splines of even degree
cites work: Factorization of Certain Piecewise Constant Matrix Functions and Its Applications
description: scientific article; zbMATH DE number 222165