A new subdivision algorithm for the flow propagation using polynomial algebras

The Jet Transport method has emerged as a powerful tool for the numerical integration of ordinary differential equations; it uses polynomial expansions to approximate the flow map associated to the differential equation in the neighbourhood of a reference solution. One of the main drawbacks of the method is that the region of accuracy becomes smaller along the integration. In this paper we introduce a procedure to determine a ball covering the set of given initial conditions that keeps the accuracy of the integration within a selected threshold. The paper gives detailed explanations of the algorithm illustrated with some examples of applicability, as well as a comparison with a previous existing method for the same purpose.