IJPAM: Volume 71, No. 2 (2011)


P.B. Vasconcelos$^1$, F.D. d'Almeida$^2$, M. Ahues$^3$
$^{1,2}$Centro de Matemática and Faculdade Economia da
Universidade do Porto
Rua Roberto Frias, 4200-465, Porto, PORTUGAL
$^3$Laboratoire de Mathématiques de l'Université de
St-Étienne, EA3989, Membre d'Université de Lyon,
23 rue Dr Paul Michelon, 42023, St-Étienne, FRANCE

Abstract. Let us consider a Fredholm integral operator and the corresponding invariant subspace basis problem. The spectral elements of the integral operator will be computed by a projection method on a subspace of dimension $n$ followed by an iterative refinement method based on defect correction. The test problem to be used is the integral formulation of the transfer problem that represents the restriction of a strongly coupled system of nonlinear equations dealing with radiative transfer in stellar atmospheres. This restriction comes from considering that the temperature and the pressure are given and makes the problem a linear one. We will describe and compare two versions for the matrix implementation of the iterative refinement method based on projection methods and defect correction. These versions differ in the basis functions considered in the discretization of the problem.

Dedicated to the memory of
Alain Largillier (1949-2010).

Received: June 11, 2011

AMS Subject Classification: 45B05, 45C05, 45E99, 65R20.

Key Words and Phrases: Fredholm integral equation, weakly singular kernel, projection approximation, iterative refinement, spectral approximation

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 71
Issue: 2