Some recent advances in validated methods for IVPs for ODEs

Compared to standard numerical methods for initial value problems (IVPs) for ordinary differential equations (ODEs), validated methods (often called interval methods) for IVPs for ODEs have two important advantages: if they return a solution to a problem, then (1) the problem is guaranteed to have a unique solution, and (2) an enclosure of the true solution is produced.We present a brief overview of interval Taylor series (ITS) methods for IVPs …