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

• Type: Technical Report
• Date: 2010

Authors

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

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