Dynibex library, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01302504
Validated Solution of Initial Value Problem for Ordinary Differential Equations based on Explicit and Implicit Runge-Kutta Schemes, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01107685
VERICOMP: a system to compare and assess verified IVP solvers, Computing, vol.24, issue.5, pp.163-172, 2012. ,
DOI : 10.1007/s00607-011-0178-4
Computing of B-series by automatic differentiation. Discrete and Continuous Dynamical Systems, pp.903-914, 2014. ,
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. ,
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
URL : https://hal.archives-ouvertes.fr/hal-00819730
HybridFluctuat: A Static Analyzer of Numerical Programs within a Continuous Environment, CAV, pp.620-626, 2009. ,
DOI : 10.1007/978-3-642-02658-4_46
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
Coefficients for the study of Runge-Kutta integration processes, Journal of the Australian Mathematical Society, vol.3, issue.5, pp.185-201, 1963. ,
A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides, ACM Transactions on Mathematical Software, vol.16, issue.3, pp.201-222, 1990. ,
DOI : 10.1145/79505.79507
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
Taylor Model Flowpipe Construction for Non-linear Hybrid Systems, 2012 IEEE 33rd Real-Time Systems Symposium, pp.183-192, 2012. ,
DOI : 10.1109/RTSS.2012.70
Self-Validated Numerical Methods and Applications, Brazilian Mathematics Colloquium, 1997. ,
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
Improving SAT modulo ODE for hybrid systems analysis by combining different enclosure methods, In SEFM LNCS, vol.7041, pp.172-187, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00630303
Error bounds for initial value problems by optimization, Soft Computing, vol.106, issue.1, pp.1345-1356, 2013. ,
DOI : 10.1007/s00500-013-1007-9
A Survey of Interval Runge???Kutta and Multistep Methods for Solving the Initial Value Problem, Parallel Processing and Applied Mathematics, pp.1361-1371, 2008. ,
DOI : 10.1007/978-3-540-68111-3_144
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
Geometric numerical integration: structure-preserving algorithms for ordinary differential equations, Computational Mathematics, 2006. ,
Solving Ordinary Differential Equations I: Nonstiff Problems, 2009. ,
DOI : 10.1007/978-3-662-12607-3
Beyond HyTech: Hybrid Systems Analysis Using Interval Numerical Methods, HSCC, pp.130-144, 2000. ,
DOI : 10.1007/3-540-46430-1_14
Rigorously computed orbits of dynamical systems without the wrapping effect, Computing, vol.66, issue.Suppl, pp.47-67, 1998. ,
DOI : 10.1007/BF02684450
Numerical Methods for Ordinary Differential Systems: The Initial Value Problem, 1991. ,
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
Enclosing the solutions of ordinary initial and boundary value problems, Computer Arithmetic, pp.255-286, 1987. ,
On the Ubiquity of the Wrapping Effect in the Computation of Error Bounds, Perspectives on Enclosure Methods, pp.201-216 ,
DOI : 10.1007/978-3-7091-6282-8_12
COSY INFINITY version 9. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers , Detectors and Associated Equipment, pp.346-350, 2006. ,
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
ONE- AND TWO-STAGE IMPLICIT INTERVAL METHODS OF RUNGE-KUTTA TYPE, Computational Methods in Science and Technology, vol.5, issue.1, pp.53-65, 1999. ,
DOI : 10.12921/cmst.1999.05.01.53-65
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
Interval Analysis, 1966. ,
Implementing a rigorous ode solver through literate programming, Modeling, Design, and Simulation of Systems with Uncertainties, pp.3-19, 2011. ,
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
An interval hermiteobreschkoff method for computing rigorous bounds on the solution of an initial value problem for an ordinary differential equation, Reliable Computing, vol.5, issue.3, pp.289-310, 1999. ,
DOI : 10.1023/A:1009936607335
A new perspective on the wrapping effect in interval methods for initial value problems for ordinary differential equations, Perspectives on Enclosure Methods, pp.219-263, 2001. ,
The Wrapping Effect, Ellipsoid Arithmetic, Stability and Confidence Regions, Validation Numerics, pp.175-190, 1993. ,
DOI : 10.1007/978-3-7091-6918-6_14
A Novel Interval Arithmetic Approach for Solving Differential-Algebraic Equations with ValEncIA-IVP, International Journal of Applied Mathematics and Computer Science, vol.19, issue.3, pp.381-397, 2009. ,
DOI : 10.2478/v10006-009-0032-4
Implementation and improvements of affine arithmetic, 2014. ,
Automatic Validation of Numerical Solutions, p.2800, 1997. ,
A Rigorous ODE Solver and Smale???s 14th Problem, Foundations of Computational Mathematics, vol.2, issue.1, pp.53-117, 2002. ,
DOI : 10.1007/s002080010018