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Error Bounds and Discretization Grids in the Solution of Weakly Singular Integral Equations

Title
Error Bounds and Discretization Grids in the Solution of Weakly Singular Integral Equations
Type
Technical Report
Year
2010
Authors
F. D. d Almeida
(Author)
FEUP
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M. Ahues
(Author)
Other
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R. Fernandes
(Author)
Other
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Scientific classification
FOS: Natural sciences > Mathematics
Associated Institutions
CMUP - CMUP - Centro de Matemática da Universidade do Porto
Other information
Abstract (EN): In the solution of weakly singular second kind Fredholm integral equations defined on the space of Lebesgue integrable complex valued functions by projection-type methods such as Kantorovitch method or Sloan method [7], the choice of the discretization grids is crucial. We will present the proof of an error bound in terms of the mesh size of the underlying discretization grid on which no regularity assumptions are made and compare it with other recently proposed error bounds [2]. This allows us to use non regular grids which is convenient when there are boundary layers or discontinuities in the right hand side function of the equation. We present some results using a simplified model of the radiative transfer in stellar atmospheres which illustrates the actual behaviour of the error in terms of the distribution of the points in the grid.
Language: English
Type (Professor's evaluation): Scientific
Reference: CMUP preprints
No. of pages: 13
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Related Publications

Of the same authors

Error Bounds and Discretization Grids in the Solution of Weakly Singular Integral Equations (2009)
Article in International Conference Proceedings Book
Filomena Dias d Almeida; M. Ahues; R. Fernandes
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