This is the second one of two companion papers. We have focused on the spectral entity determination in the first paper where we have considered the Hilbert-Schmidt and Pincherle-Goursat kernels. The basic idea has been the development of a perturbation expansion around the zero interval limit therein. We have emphasized on the case of most dominant eigenvalue and corresponding eigenfunction by taking the half-interval length as the perturbation parameter after universalizing the given (finite) interval of the integral operator. The basic issues in the formulation of the perturbation expansion and certain technicalities were kept as the main theme of the paper in the first companion paper. This second companion paper, however, has been designed to focus on the convergence discussions and confirmative implementations. It also presents a numerical comparison between proposed method and various well known approximation methods residing in scientific literature.