On the Numerical Computation of Eigenvalues and Eigenfunctions of Compact Integral Operators Using Spline Functions†

摘要

This paper is concerned with computing accurate approximations to the eigen values and eigenfunctions of linear integral operators. The spline-collocation method is given for obtaining approximate solutions of the class of weakly singular compact operators. The method consists of representing the approximate eigenfunctions of the given problem by spline functions and using collocation to reduce the given problem to a standard matrix eigenvalue problem. The relationship between the Nystrom method and the collocation method is studied. Finally, several numerical examples which demonstrate the efficiency of the Nystrom method and the proposed method are presented.