HybridFluctuat: A Static Analyzer of Numerical Programs within a Continuous Environment
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Proving the Correctness of the Implementation of a Control-Command Algorithm
SAS '09 Proceedings of the 16th International Symposium on Static Analysis
Abstract interpretation of the physical inputs of embedded programs
VMCAI'08 Proceedings of the 9th international conference on Verification, model checking, and abstract interpretation
A hybrid denotational semantics for hybrid systems
ESOP'08/ETAPS'08 Proceedings of the Theory and practice of software, 17th European conference on Programming languages and systems
Computing bounded reach sets from sampled simulation traces
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
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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.