TY - GEN
T1 - Enclosing temporal evolution of dynamical systems using numerical methods
AU - Bouissou, Olivier
AU - Chapoutot, Alexandre
AU - Djoudi, Adel
PY - 2013/9/9
Y1 - 2013/9/9
N2 - Numerical methods are necessary to understand the behaviors of complex hybrid systems used to design control-command systems. Especially, numerical integration methods are heavily used in simulation to compute approximations of the solution of differential equations, including non-linear and stiff solutions. Nevertheless, these methods only produce approximate results and they should not be used in formal verification methods as is. We propose a systematic way to make explicit Runge-Kutta integration method safe with respect to the mathematical solution. As side effect, we can hence compare different integration schemes in order to pick the right one in different situations.
AB - Numerical methods are necessary to understand the behaviors of complex hybrid systems used to design control-command systems. Especially, numerical integration methods are heavily used in simulation to compute approximations of the solution of differential equations, including non-linear and stiff solutions. Nevertheless, these methods only produce approximate results and they should not be used in formal verification methods as is. We propose a systematic way to make explicit Runge-Kutta integration method safe with respect to the mathematical solution. As side effect, we can hence compare different integration schemes in order to pick the right one in different situations.
UR - https://www.scopus.com/pages/publications/84883316652
U2 - 10.1007/978-3-642-38088-4_8
DO - 10.1007/978-3-642-38088-4_8
M3 - Conference contribution
AN - SCOPUS:84883316652
SN - 9783642380877
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 108
EP - 123
BT - NASA Formal Methods - 5th International Symposium, NFM 2013, Proceedings
T2 - 5th International Symposium on NASA Formal Methods, NFM 2013
Y2 - 14 May 2013 through 16 May 2013
ER -