Wrapping Function of the Initial Value Problem for ODE: Applications

Abstract

We discuss applications of the concept of wrapping function in studying the wrapping effect associated with validated (interval) methods for numerical solution of the initial value problem for ordinary differential equations. Initial value problems are characterized with respect to the occurrence of wrapping effect using that there is no wrapping effect if and only if the wrapping function equals the optimal interval enclosure of the solution. Particular attention is paid to linear systems of ODEs where the functions quantifying the wrapping effect can be presented in a simpler form. A necessary condition for no wrapping effect is proved for the general case.