Pseudosingularity in the eigenvalue integral equations

TL;DR

This paper investigates pseudosingularities in eigenvalue integral equations, revealing their impact on numerical solution reliability and discussing related phenomena affecting solution accuracy.

Contribution

It identifies and analyzes pseudosingularities in eigenvalue integral equations, highlighting their effects on numerical solution reliability and introducing related odd phenomena.

Findings

Pseudosingularities impair numerical solution reliability

Odd phenomena emerge in numerical eigenvalues and eigenfunctions

Relations between pseudosingularities and solution accuracy are discussed

Abstract

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.