The Method of Shrink Wrapping For the Validated Solution of ODEs

In this note, we outline one method to perform shrink wrapping to eliminate the remainder term of the Taylor model integration of ODEs. We point out that there are many variants of this approach, and while the one shown here is perhaps the simplest one to understand, it is not necessarily the optimal choice. More about other possibilities at the end of the section. After the n-th step of the integration, the region occupied by the final variables is given by the set