Quasinilpotency of the operators in picard-lindelöf iteration

Abstract

The superlinear convergence of Picard-Lindelöf iteration on finite time intervals is studied by considering the resolvent operator as an operator-valued entire function. The main conclusions of this paper are related to the following fact: the convergence properties of the iteration when applied to a large and sparse system are largely determined by the graph properties of the decomposition and are partly insensitive in terms of the values of the elements of the matrices.