From: Prasanth Nair <P.B.Nair@soton.ac.uk_SPAMBLOCK>
Subject: Re: eigenfunctions of a integral equation
Date: Mon, 27 Sep 1999 20:19:16 +0100
Newsgroups: sci.math.num-analysis
Keywords: homogeneous Fredholm integral equation

"Moo K. Chung" wrote:

> The problem is
>
>  \int R(t,s)f(s) ds = c^2f(t)
>
> and need to find n-th eigenfunction corresponding to n-th eigenvalue of
> decreasing order numerically. Any pointer would be appreciated.

This is a homogeneous Fredholm integral equation of the second
kind. This integral eigenvalue problem can be solved analytically
for a class of correlation functions (R(t,s)) defined on simple
domains, such as a line, square, etc. A Galerkin procedure can be
used to compute the eigenparameters numerically if an analytical
solution is not possible.

A detailed description including references can be found in
Chapter 2 of the book - R.G. Ghanem and P.D. Spanos,
STOCHASTIC FINITE ELEMENTS:  A Spectral Approach.
See also Chapter 5 for some example problems.

This book is available online at -
http://venus.ce.jhu.edu/book/book.html
The relevant section is -
http://venus.ce.jhu.edu/book/chp2/node11.html#SECTION00133000000000000000

Hope this helps.

Prasanth
-
---------------------------------------
Prasanth B. Nair
Computational Engineering and Design Center
University of Southampton, Highfield
Southampton SO17 1BJ,  U.K.
Phone : +44-1703-595068
Fax   : +44-1703-593230
email : P.B.Nair@soton.ac.uk
WWW   : http://www.soton.ac.uk/~pbn
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