J. Alexandre, D. Sandretto, and A. Chapoutot, Validated Explicit and Implicit Runge-Kutta Methods, Reliable Computing, vol.22, pp.79-103, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01111240

F. Benhamou, D. Mcallester, and P. Van-hentenryck, CLP (Intervals ) Revisited, 1994.

F. Bornemann, Runge-Kutta Methods, Trees, and Maple -On a Simple Proof of Butcher's Theorem and the Automatic Generation of Order Condition, Selcuk Journal of Applied Mathematics, vol.2, issue.1, 2001.

C. John and . Butcher, Coefficients for the Study of Runge-Kutta Integration Processes, Journal of the Australian Mathematical Society, vol.3, pp.185-201, 1963.

C. John and . Butcher, Numerical Methods for Ordinary Differential Equations, 2003.

G. Chabert and L. Jaulin, Contractor programming, Artificial Intelligence, vol.173, issue.11, pp.1079-1100, 2009.
DOI : 10.1016/j.artint.2009.03.002

URL : https://hal.archives-ouvertes.fr/hal-00428957

L. Euler, Institutiones Calculi Integralis, Academia Imperialis Scientiarum, p.1792

T. Feagin, High-order Explicit Runge-Kutta Methods Using M-Symmetry, Neural, Parallel & Scientific Computations, vol.20, issue.4, pp.437-458, 2012.

A. Griewank, Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, Society for Industrial and Applied Mathematics, 2000.
DOI : 10.1137/1.9780898717761

E. Hairer, S. P. Norsett, and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems, 2009.
DOI : 10.1007/978-3-662-12607-3

E. R. Hansen, AN OVERVIEW OF GLOBAL OPTIMIZATION USING INTERVAL ANALYSIS
DOI : 10.1016/B978-0-12-505630-4.50021-3

L. Jaulin, M. Kieffer, O. Didrit, and E. Walter, Applied Interval Analysis, 2001.
DOI : 10.1007/978-1-4471-0249-6

URL : https://hal.archives-ouvertes.fr/hal-00845131

W. Martin and . Kutta, Beitrag zur Näherungsweisen Integration Totaler Differentialgleichungen, Zeit. Math. Phys, vol.46, pp.435-53, 1901.

Y. Lebbah and O. Lhomme, Accelerating filtering techniques for numeric CSPs, Artificial Intelligence, vol.139, issue.1, pp.109-132, 2002.
DOI : 10.1016/S0004-3702(02)00194-7

O. Lhomme, Consistency Techniques for Numeric CSPs, Proceedings of the 13th International Joint Conference on Artifical Intelligence, pp.232-238, 1993.

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

J. Martín-vaquero, A 17th-order Radau IIA method for package RADAU. Applications in mechanical systems, Computers & Mathematics with Applications, vol.59, issue.8, 2010.
DOI : 10.1016/j.camwa.2009.12.025

R. Moore, Interval Analysis, 1966.

J. Muller, N. Brisebarre, F. De-dinechin, C. Jeannerod, V. Lefèvre et al., Handbook of Floating-Point Arithmetic, Nathalie Revol, 2009.
DOI : 10.1007/978-0-8176-4705-6

URL : https://hal.archives-ouvertes.fr/ensl-00379167

A. Ralston, Runge-Kutta Methods with Minimum Error Bounds Mathematics of computation, pp.431-437, 1962.

M. Rueher, Solving Continuous Constraint Systems, Proc. of 8th International Conference on Computer Graphics and Artificial Intelligence (3IA'2005), 2005.