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

• Type: Article in International Conference Proceedings Book
• Date: 2009

Authors

Filomena Dias d Almeida (Author) FEUP; M. Ahues (Author) Other; R. Fernandes (Author) Other

Conference proceedings International

Title: 2nd Dolomites Workshop on Constructive Approximation and Applications. Book of abstracts

Pages: 67-67

2nd Dolomites Workshop on Constructive Approximation and Applications

Alba di Canazei (1517 m), Val di Fassa (Trento), Italy, September 4–9, 2009

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Abstract (EN): Error Bounds and Discretization Grids in the Solution of Weakly Singular Integral Equations∗ F. D. d’Almeida† Universidade do Porto, Portugal M. Ahues‡ Universit´e de Saint-´Etienne, France R. Fernandes§ Universidade do Minho, Portugal 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 Petrov-Galerkin or Kantorovitch methods [1], 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 wiht 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. References [1] K. Atkinson, The numerical solution of integral equations of the second kind, n. 4 in Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, 1997. [2] M. Ahues, A. Amosov, A. Largillier, Superconvergence of some projection approximations for weakly singular integral equations using general grids, SIAM J. Numer. Anal. 47 (2009), no. 1, 646–674 ¤

Language: English

Type (Professor's evaluation): Scientific