@inproceedings{cha-ale-mul-15-aa-runge,
  author = {Chapoutot, Alexandre and Alexandre dit Sandretto, Julien and Mullier, Olivier},
  title = {Validated Explicit and Implicit {Runge}-{Kutta} Methods},
  booktitle = {Proceedings of the Small Workshop on Interval Methods},
  location = {Prague, CZ},
  year = 2015,
  month = jun,
  comment = {Uses Taylor analysis of Runge-Kutta (after John Butcher) and ``some'' validated arithmetic. Lists AA as a keyword but does not mention it explicitly in the article.},
  abstract = {The guaranteed solution of initial value problem of ordinary differential equations is well studied from interval analysis community. In the most of the cases Taylor models are used in this context, see [1] and the references therein. In contrast, in numerical analysis community other numerical integration methods, e.g., Runge-Kutta methods, are used. Indeed, these methods have very good stability properties [2] and they can be applied on a wide variety of problems. We propose a new method to validate the solution of initial value problem of ordinary differential equations based on Runge-Kutta methods. The strength of our contribution is to adapt any explicit and implicit Runge-Kutta methods to make them guaranteed. We experimentally verify our approach against Vericomp benchmark2 and the results are reported in [3].}
}