Validated solutions of initial value problems for ordinary differential equations
Compared to standard numerical methods for initial-value problems (IVPs) for ordinary
differential equations (ODEs), validated methods for IVPs for ODEs have two important …
differential equations (ODEs), validated methods for IVPs for ODEs have two important …
Validated solutions of initial value problems for parametric ODEs
Y Lin, MA Stadtherr - Applied Numerical Mathematics, 2007 - Elsevier
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 …
desirable in many applications to be able to determine a validated enclosure of all possible …
Taylor forms—use and limits
A Neumaier - Reliable computing, 2003 - Springer
This review is a response to recent discussions on the reliable computing mailing list, and to
continuing uncertainties about the properties and merits of Taylor forms, multivariate higher …
continuing uncertainties about the properties and merits of Taylor forms, multivariate higher …
An effective high-order interval method for validating existence and uniqueness of the solution of an IVP for an ODE
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 …
bounds that are guaranteed to contain the true solution of a problem. When computing such …
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 …
differential equations (ODEs), validated methods (often called interval methods) for IVPs for …
On Taylor model based integration of ODEs
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 …
used for more than 40 years. For many classes of IVPs, these methods are able to compute …
Unified framework for the propagation of continuous-time enclosures for parametric nonlinear ODEs
This paper presents a framework for constructing and analyzing enclosures of the reachable
set of nonlinear ordinary differential equations using continuous-time set-propagation …
set of nonlinear ordinary differential equations using continuous-time set-propagation …
Computing reachable sets for uncertain nonlinear hybrid systems using interval constraint-propagation techniques
We investigate solution techniques for numerical constraint-satisfaction problems and
validated numerical set integration methods for computing reachable sets of nonlinear …
validated numerical set integration methods for computing reachable sets of nonlinear …
Convex/concave relaxations of parametric ODEs using Taylor models
This paper presents a discretize-then-relax method to construct convex/concave bounds for
the solutions of a wide class of parametric nonlinear ODEs. The algorithm builds upon …
the solutions of a wide class of parametric nonlinear ODEs. The algorithm builds upon …
Deterministic global optimization of nonlinear dynamic systems
Y Lin, MA Stadtherr - AIChE Journal, 2007 - Wiley Online Library
A new approach is described for the deterministic global optimization of dynamic systems,
including optimal control problems. The method is based on interval analysis and Taylor …
including optimal control problems. The method is based on interval analysis and Taylor …