Eigenpairs of Fredholm Integral Operators With Separable Kernel
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Date
2012-02-02
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Addis Ababa University
Abstract
An integral equation is an equation in which the unknown function appears in the integrand.
There are different types of integral equations, among these Fredholm integral equation is an
integral equation with constant limit of integration. Depending on the appearance of the
unknown function we have three kinds of Fredholm integral equations, first kind, second
kind and third kind.
In this project we discuss the techniques of solving Fredholm integral equations. Even
though, it is difficult to find the solution of each kind, we consider the solution of the first
kind in terms of a linear combination of eigenpairs of separable kernel. The solution of the
second kind is also determined by using different decomposition methods.
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Keywords
Eigenpairs, Fredholm Integral, Operators, Separable Kernel