J. Alexandre, A. Sandretto, and . Chapoutot, Validated explicit and implicit Runge-Kutta methods. Reliable Computing, vol.22, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01111240

Y. Bertot, G. Gonthier, S. O. Biha, and I. Pasca, Canonical big operators, International Conference on Theorem Proving in Higher Order Logics, pp.86-101, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00331193

M. Berz and K. Makino, Verified integration of ODEs and flows using differential algebraic methods on high-order Taylor models, Reliable Computing, vol.4, issue.4, pp.361-369, 1998.

S. Boldo, Floats & Ropes : a case study for formal numerical program verification, 36th International Colloquium on Automata, Languages and Programming, vol.5556, pp.91-102, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00432718

S. Boldo, F. Clément, J. Filliâtre, M. Mayero, G. Melquiond et al., Wave Equation Numerical Resolution : a Comprehensive Mechanized Proof of a C Program, Journal of Automated Reasoning, vol.50, issue.4, pp.423-456, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00649240

S. Boldo, F. Faissole, and A. Chapoutot, Round-off Error Analysis of Explicit One-Step Numerical Integration Methods, 24th IEEE Symposium on Computer Arithmetic, pp.82-89, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01581794

S. Boldo and G. Melquiond, Computer Arithmetic and Formal Proofs, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01632617

O. Bouissou and M. Martel, GRKLib : a guaranteed Runge-Kutta library, International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics, 2006.

L. Fousse, Multiple-precision correctly rounded Newton-Cotes quadrature, ITA, vol.41, issue.1, pp.103-121, 2007.
URL : https://hal.archives-ouvertes.fr/inria-00106151

P. Henrici, Error propagation for difference methods. The SIAM series in applied mathematics, 1963.

N. J. Higham, Accuracy and Stability of Numerical Algorithms, Society for Industrial and Applied Mathematics, 2002.

, IEEE standard for floating-point arithmetic, IEEE Std, pp.754-2008, 2008.

F. Immler and J. Hölzl, Numerical analysis of ordinary differential equations in Isabelle/HOL, Interactive Theorem Proving, vol.7406, pp.377-392, 2012.

F. Immler and C. Traut, The flow of ODEs : Formalization of Variational Equation and Poincaré Map, Journal of Automated Reasoning, vol.62, issue.2, pp.215-236, 2019.

A. Mahboubi and E. Tassi, Mathematical Components, 2017.

G. Melquiond, Proving bounds on real-valued functions with computations, International Joint Conference on Automated Reasoning, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00180138

M. Neher, K. R. Jackson, and N. S. Nedialkov, On Taylor model based integration of ODEs, SIAM Journal on Numerical Analysis, vol.45, issue.1, pp.236-262, 2007.

P. Roux, Formal Proofs of Rounding Error Bounds -With Application to an Automatic Positive Definiteness Check, J. Autom. Reasoning, vol.57, issue.2, pp.135-156, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01091189