R. E. Moore, Interval Analysis. Series in Automatic Computation, 1966.

N. S. Nedialkov, K. R. Jackson, and G. F. Corliss, Validated solutions of initial value problems for ordinary differential equations, Applied Mathematics and Computation, vol.105, issue.1, pp.21-68, 1999.
DOI : 10.1016/S0096-3003(98)10083-8

K. Makino and M. Berz, COSY INFINITY version 9. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, pp.346-350, 2006.

Y. Lin and M. A. Stadtherr, Validated solutions of initial value problems for parametric ODEs, Applied Numerical Mathematics, vol.57, issue.10, pp.1145-1162, 2007.
DOI : 10.1016/j.apnum.2006.10.006

T. Dzetkuli?, Rigorous integration of non-linear ordinary differential equations in chebyshev basis, Numerical Algorithms, vol.2, issue.1, pp.183-205, 2015.
DOI : 10.1007/s11075-014-9889-x

K. Gajda, A. Marciniak, and B. Szyszka, THREE- AND FOUR-STAGE IMPLICIT INTERVAL METHODS OF RUNGE-KUTTA TYPE, Computational Methods in Science and Technology, vol.6, issue.1, pp.41-59, 2000.
DOI : 10.12921/cmst.2000.06.01.41-59

A. Marciniak and B. Szyszka, ON REPRESENTATIONS OF COEFFICIENTS IN IMPLICIT INTERVAL METHODS OF RUNGE-KUTTA TYPE, Computational Methods in Science and Technology, vol.10, issue.1, pp.57-71, 2004.
DOI : 10.12921/cmst.2004.10.01.57-71

A. Marciniak, Implicit Interval Methods for Solving the Initial Value Problem, Numerical Algorithms, vol.37, issue.1-4, pp.241-251, 2004.
DOI : 10.1023/B:NUMA.0000049471.81341.60

O. Bouissou and M. Martel, GRKLib: a Guaranteed Runge Kutta Library, 12th GAMM, IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006), 2006.
DOI : 10.1109/SCAN.2006.20

O. Bouissou, A. Chapoutot, and A. Djoudi, Enclosing Temporal Evolution of Dynamical Systems Using Numerical Methods, NASA Formal Methods, number 7871 in LNCS, pp.108-123, 2013.
DOI : 10.1007/978-3-642-38088-4_8

E. Hairer, C. Lubich, and G. Wanner, Geometric numerical integration: structure-preserving algorithms for ordinary differential equations, Computational Mathematics, 2006.

C. John and . Butcher, Coefficients for the study of Runge-Kutta integration processes, Journal of the Australian Mathematical Society, vol.3, issue.5, pp.185-201, 1963.

F. Bartha, Z. Hans, and . Munthe-kaas, Computing of B-series by automatic differentiation. Discrete and continuous dynamical systems, pp.903-914, 2014.

A. Chapoutot, J. Alexandre, O. Sandretto, and . Mullier, Validated Explicit and Implicit Runge-Kutta Methods, Small Workshop on Interval Methods, 2015.

A. Griewank, J. Utke, and A. Walther, Evaluating higher derivative tensors by forward propagation of univariate Taylor series, Mathematics of Computation, vol.69, issue.231, pp.1117-1130, 2000.
DOI : 10.1090/S0025-5718-00-01120-0