Rate of convergence of local linearization schemes for initial-value problems

There is a large variety of Local Linearization (LL) schemes for the numerical integration of initial-value problems, which differ with respect to the algorithm that is used in the numerical implementation of the Local Linear Discretization. However, in contrast with the LL Discretization, the order of convergence of the LL schemes have not been studied so far. In this paper, a general result about that matter is given. In addition, a brief survey of the main implementations of the LL method is also presented.