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Errors and grids for projected weakly singular integral equations

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Resumo:In the solution of weakly singular Fredholm integral equations of the second kind defined on the space of Lebesgue integrable complex valued functions by projection methods, the choice of the grid 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. This proof generalizes the work done for the Galerkin method, to the case of Kantorovich and Sloan methods. This allows us to use nonuniform grids when there are boundary layers or discontinuities in the right hand side of the equation. We illustrate this with an example on the radiative transfer model in stellar atmospheres.
Autores principais:Almeida, Filomena Dias d'
Outros Autores:Ahues, Mario; Fernandes, Rosário
Assunto:Projection approximations in L^1 Weakly singular integral operators Nonuniform grids Error bounds Ciências Naturais::Matemáticas
Ano:2013
País:Portugal
Tipo de documento:artigo
Tipo de acesso:acesso restrito
Instituição associada:Universidade do Minho
Idioma:inglês
Origem:RepositóriUM - Universidade do Minho

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