A degenerate kernel method for eigenvalue problems of compact integral operators

We consider the approximation of eigenfunctions of a compact integral operator with a smooth kernel by a degenerate kernel method. By interpolating the kernel of the integral operator in both the variables, we prove that the error bounds for eigenvalues and for the distance between the spectral subspaces are of the orders $h^{2r}$ and $h^r$ respectively. By iterating the eigenfunctions we show that the error bounds for eigenfunctions are of the orders $h^{2r}$.We give the numerical results