AbstractThe aim of this paper is to approximate the solution of a class of
integral equations of the third kind on an unbounded domain. For
computing such approximation, the collocation method based on the
generalized Laguerre abscissas is considered. In this method, the
unknown function is interpolated at the nodal points
${\lbrace t_i\rbrace _{i=1}^{n+1}}$, where ${\lbrace t_i\rbrace _{i=1}^{n}}$ are the zeros of
generalized Laguerre polynomials and ${t_{n+1}=4n}$. Then, the given
equation is transformed to the Fredholm integral equation of the
second kind. In the sequel, according to the integration interval,
we apply the Gauss–Laguerre collocation method on the interval
${[0,\infty )}$ by using the given nodal points. Therefore, the
solution of the third kind integral equation is reduced to the
solution of a system of linear equations. Convergence analysis of
the method in some Sobolev-type space is studied. Illustrative
examples are included to demonstrate the validity and applicability
of the technique.
