Validated method for IVPs for Ordinary Differential Equations based on Chaplygin's inequalities

Standard numerical methods for initial value problems (IVPs) for odinary differential equations (ODEs) return approximate solution only. Validated (also called interval) methods for IVPs for ODEs return approximate solution together with a rigorous enclosure of the true solution. A widely known validated method for IVPs for ODEs is the interval Hermite-Obreschkoff (IHO). This method meets the difficulties on stiff ODEs. The method of Chaplygin's inequalities is less known. However, it might be more suitable for problems like interval Spice simulator, because electrical circuits are described in Spice by stiff emprical ODEs which are not smooth enough. This memo describes IHO and Chaplygin validated methods and studies their stability on a simple ODE dy/dt=-y.