@inproceedings{bou-cha-djo-13-aa-runge,
  author = {Bouissou, Olivier and Chapoutot, Alexandre and Djoudi, Adel},
  title = {Enclosing temporal evolution of dynamical systems using numerical methods},
  booktitle = {Proceedings of the 5th International NASA Symposium on Formal Methods (NFM)},
  location = {Moffett Field, US},
  series = {Lecture Notes in Computer Science},
  volume = {7871},
  isbn = {978-3-642-38087-7},
  year = 2013,
  month = may,
  pages = {108-123},
  doi = {10.1007/978-3-642-38088-4_8},
  comment = {Uses AA for reliable Runge-Kutta.},
  abstract = {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.}
}