Galerkin methods for eigenvalue problem of an integral operator with logarithmic kernel

Abstract

In this paper, we consider the singularity preserving Galerkin methods to solve the eigenvalue problem of a compact integral operator on a Banach space with the logarithmic kernel. In this method, the projected space is chosen as the direct sum of singular subspace and spline function subspace. We establish the convergence rates for the gap between the spectral subspaces, and the optimal order of convergence for eigenvalues and iterated eigenvectors. We illustrate our results with a numerical example.