In the present paper we use a recently proposed generalization of the Hukuhara difference
for compact convex sets, to introduce and study a generalization of the Hukuhara …

A detailed comparison between Taylor model methods and other tools for validated
computations is provided. Basic elements of the Taylor model (TM) methods are reviewed …

Since the creation of the digital computer, numerical computations have played an
increasingly fundamental role in modeling physical phenomena for science and …

In initial value problems for ODEs with interval-valued parameters and/or initial values, it is
desirable in many applications to be able to determine a validated enclosure of all possible …

This paper investigates the use of guaranteed methods to perform state and parameter
estimation for nonlinear continuous-time systems, in a bounded-error context. A state …

Compared to standard numerical methods for initial value problems (IVPs) for ordinary
differential equations (ODEs), validated methods (often called interval methods) for IVPs for …

Interval methods for verified integration of initial value problems (IVPs) for ODEs have been
used for more than 40 years. For many classes of IVPs, these methods are able to compute …

We overview the current state of interval methods and software for computing bounds on
solutions in initial value problems (IVPs) for ordinary differential equations (ODEs). We …

Further to a recent controversy on whether the differential transformation method (DTM) for
solving a differential equation is purely and solely the traditional Taylor series method, it is …

In this paper, we show how to compute an over-approximation for the reachable set of
uncertain nonlinear continuous dynamical systems by using guaranteed set integration. We …