Abstract: This paper discusses the reliability of the numerical solution to a Fredholm integral equation of the first kind. Although a stable system of linear equations can be obtained from the integral equation of the first kind in the Fabry-Perot inverse interfe rence spectroscopy, by using the simplest rectangle formula, in the case △e=2/x, △x=2/e and the number of equally-spaced sampling points being a suitable odd one, its solution is not the solution to the original integral equation. That is to say, the stable numerical solution is not reliable.

Key words: reliability of numerical solution, Fredholm integral equation of the first kind, inverse interference spectroscopy