  The reliability is of the most importance when employing a numerical method
to solve the eigenvalue integral equations. In this paper, we present one type
of particular singularities (pseudosingularities) existing in eigenvalue
integral equations which will impair even destroy the reliability of the
numerical solutions in an implicit way. Two odd phenomena emerging in the
numerical eigenvalues and the corresponding eigenfunctions are reviewed. And
the relations between the pseudosingularities, the odd phenomena and the
reliability of the obtained numerical results are discussed.
