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The iterated projection solution for the Fredholm integral equation of second kind

Published online by Cambridge University Press:  17 February 2009

Françoise Chatelin  and
Rachid Lebbar
Rachid Lebbar
Affiliation:
Université de Grenoble, Mathématiques Appliquées, IMAG, BP 53X, 38041 GRENOBLE-CEDEX, France
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Abstract

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We are concerned with the solution of the second kind Fredholm equation (and eigenvalue problem) by a projection method, where the projection is either an orthogonal projection on a set of piecewise polynomials or an interpolatory projection at the Gauss points of subintervals.

We study these cases of superconvergence of the Sloan iterated solution: global superconvergence for a smooth kernel, and superconvergence at the partition points for a kernel of “Green's function” type. The mathematical analysis applies for the solution of the inhomogeneous equation as well as for an eigenvector.

Type
Research Article
Information
The ANZIAM Journal , Volume 22 , Issue 4 , April 1981 , pp. 439 - 451
Copyright
Copyright © Australian Mathematical Society 1981

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