GRKLib
GRKLib: a Guaranteed Runge Kutta Library. In this article, we describe a new library for computing guaranteed bounds of the solutions of Initial Value Prob- lems (IVP). Given an initial value problem and an end point, our library computes a sequence of approximation points together with a sequence of approximation errors such that the distance to the true solution of the IVP is below these er- ror terms at each approximation point. These sequences are computed using a classical Runge-Kutta method for which truncation and roundoff errors may be over-approximated. We also compute the propagation of local errors to obtain an enclosure of the global error at each computation step. These techniques are implemented in a C++ library which provides an easy-to-use framework for the rigorous approx- imation of IVP. This library implements an error control technique based on step size reduction in order to reach a certain tolerance on local errors.
Keywords for this software
References in zbMATH (referenced in 6 articles )
Showing results 1 to 6 of 6.
Sorted by year (- Le Coënt, Adrien; Alexandre dit Sandretto, Julien; Chapoutot, Alexandre; Fribourg, Laurent: An improved algorithm for the control synthesis of nonlinear sampled switched systems (2018)
- Huang, Zhenqi; Fan, Chuchu; Mitra, Sayan: Bounded invariant verification for time-delayed nonlinear networked dynamical systems (2017)
- Alexandre dit Sandretto, Julien; Chapoutot, Alexandre; Mullier, Olivier: Tuning PI controller in non-linear uncertain closed-loop systems with interval analysis (2015)
- Cortesi, Agostino; Costantini, Giulia; Ferrara, Pietro: The abstract domain of trapezoid step functions (2015)
- Huang, Zhenqi; Mitra, Sayan: Computing bounded reach sets from sampled simulation traces (2012)
- Bouissou, Olivier: Proving the correctness of the implementation of a control-command algorithm (2009)