Linear Acceleration of Picard-Lindelöf Iteration.
The class of linear differential systems with coefficient matrices which are commutative with their integrals is considered. The results on asymptotic equivalence of these systems and their distribution among linear systems are given.
In the paper existence and uniqueness results for the linear differential system on the interval [0,1] with distributional coefficients and solutions from the space of regulated functions are obtained.
Given a second order differential equation on a manifold we find necessary and sufficient conditions for the existence of a coordinate system in which the system is linear. The main tool to be used is a linear connection defined by the system of differential equations.