An interpolation degenerate kernel method for eigenvalue problems of a class of non-compact operators

Abstract

We consider the eigenvalue problem of a class of non-compact linear operators given as the sum of a multiplication and a kernel operator. A degenerate kernel method with piecewise constant interpolation with respect to the second variable is used to approximate isolated eigenvalues of finite type. The convergence of the method is proved, and it is shown that the error is of order O ( h ) . The proposed method has been applied to some sample problems.