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Pseudosingularity in the eigenvalue integral equations

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.