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On Spline Approximation for Singular Integral Equations on an Interval
Author(s) -
Elschner Johannes
Publication year - 1988
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19881390128
Subject(s) - mathematics , piecewise , spline (mechanical) , sobolev space , mathematical analysis , degree of a polynomial , weight function , degree (music) , polynomial , physics , structural engineering , engineering , acoustics
This paper analyses the convergence of spline approximation methods for strongly elliptic singular integral equations on a finite interval. We consider collocation by smooth polynomial splines of odd degree multiplied by a weight function and a Galerkin‐Petrov method with spline trial functions of even degree and piecewise constant test functions. We prove the stability of the methods in weighted Sobolev spaces and obtain the optimal orders of convergence in the case of graded meshes.