Abstract

The Gaussian and its generalization known as the Laguerre-Gaussians are used in this paper as a collocation basis for Fredholm integral equations of the second kind. The collocation points are chosen so that they coincide with the points around with the interpolant is translated. This leads to a linear system whose solution gives the coefficients of the interpolant. In this study, we have used two examples to illustrate the proposed method and the comparison between exact and numerical solutions shows that the proposed method provides a good approximation to the exact solution.

Key words: Gaussians, Laguerre-Gaussians, Fredholm integral equations, collocation.