We present the CAPD:: DynSys library for rigorous numerical analysis of dynamical systems.
The basic interface is described together with several interesting case studies illustrating …

This book is designed to be used by mathematicians, engineers, and computer scientists as
a graduate-level introduction to numerical analysis and its methods. Readers are expected …

A set of validated numerical integration methods based on explicit and implicit Runge-Kutta
schemes is presented to solve, in a guaranteed way, initial value problems of ordinary …

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

Validated methods for initial value problems for ordinary differential equations produce
bounds that are guaranteed to contain the true solution of a problem. When computing such …

We present a modification of the Lohner algorithm for the computation of rigorous bounds for
solutions of ordinary differential equations together with partial derivatives with respect to …

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 …

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 …

This paper presents a framework for constructing and analyzing enclosures of the reachable
set of nonlinear ordinary differential equations using continuous-time set-propagation …