Convergence of the Arnoldi process when applied to the Picard-Lindelِf iteration operator

In this paper the iteration operator corresponding to the Picard-Lindelِf iteration is considered as a model case in order to investigate the convergence theory of the Arnoldi process. We ask whether it is possible to use a theorem by Nevanlinna and Vainikko to obtain the spectrum of the local operator. In the case considered here the answer is no.