From: Prasanth Nair
Subject: Re: eigenfunctions of a integral equation
Date: Mon, 27 Sep 1999 20:19:16 +0100
Newsgroups: sci.math.numanalysis
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 nth eigenfunction corresponding to nth 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 : +441703595068
Fax : +441703593230
email : P.B.Nair@soton.ac.uk
WWW : http://www.soton.ac.uk/~pbn
