Errors and grids for projected weakly singular integral equations

• Type: Article in International Scientific Journal
• Date: 2013

Authors

d'Almeida, F.D. (Author) FEUP; Ahues, M. (Author) Other; Fernandes, R. (Author) Other

Journal

Title: International Journal of Pure and Applied Mathematics

Vol. 89

Pages: 203-213

ISSN: 1311-8080

Publisher: Academic Publications Ltd

Indexing

ISI Web of Knowledge

Scopus - 3 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-008-JQQ

DOI: 10.12732/ijpam.v89i2.6

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 11