We consider an integral operator with a kernel of the Green's function type. We prove the existence of asymptotic expansion of an eigenvalue of multiplicity $m>1$, when the integral operator is approximated by the iterated Galerkin operator. This enables us to use the Richardson extrapolation to increase the order of convergence of the eigenvalue. We consider a numerical example to illustrate our theoretical results.
"Asymptotic expansions for approximate eigenvalues of integral operators with nonsmooth kernels of multiplicity $m>1$." J. Integral Equations Applications 31 (3) 411 - 430, 2019. https://doi.org/10.1216/JIE-2019-31-3-411