[Auer, E., Rauh, A., Hofer, E. P. and Luther, W. (2008). Validated modeling of mechanical systems with SmartMOBILE: Improvement of Performance by ValEncIA-IVP, Proceedings of the Dagstuhl Seminar 06021—Reliable Implementation of Real Number Algorithms: Theory and Practice, Dagstuhl, Germany, Lecture Notes in Computer Science, Vol. 5045, Springer-Verlag, Berlin/Heidelberg, pp. 1-27.]Search in Google Scholar
[Bendsten, C. and Stauning, O. (2007). FADBAD++, Version 2.1, Available at: http://www.fadbad.com]Search in Google Scholar
[Berz, M. and Makino, K. (1998). Verified integration of ODEs and flows using differential algebraic methods on highorder Taylor models, Reliable Computing 4(4): 361-369.10.1023/A:1024467732637]Search in Google Scholar
[Cash, J. R. and Considine, S. (1992). An MEBDF code for stiff initial value problems, ACM Transactions on Mathematical Software (TOMS) 18(2): 142-155.10.1145/146847.146922]Search in Google Scholar
[Chua, L., Desoer, C. A. and Kuh, E. S. (1990). Linear and Nonlinear Circuits, McGraw-Hill, New York, NY.]Search in Google Scholar
[Czechowski, P. P., Giovannini, L. and Ordys, A. W. (2006). Testing algorithms for inverse simulation, Proceedings of the 2006 IEEE International Conference on Control Applications, Munich, Germany, pp. 2607-2612.]Search in Google Scholar
[de Swart, J. J. B., Lioen, W. M. and van der Veen, W. A. (1998). Specification of PSIDE, Technical Report MAS-R9833, CWI, Amsterdam, Available at: http://walter.lioen.com/papers/SLV98.pdf]Search in Google Scholar
[Deville, Y., Janssen, M. and van Hentenryck, P. (2002). Consistency techniques for ordinary differential equations, Constraint 7(3-4): 289-315.10.1023/A:1020573518783]Search in Google Scholar
[Eijgenraam, P. (1981). The solution of initial value problems using interval arithmetic, Mathematical Centre Tracts No. 144, Stichting Mathematisch Centrum, Amsterdam.]Search in Google Scholar
[Galassi, M. (2006). GNU Scientific Library Reference Manual. Revised Second Edition (v1.8), Available at: http://www.gnu.org/software/gsl/]Search in Google Scholar
[Hairer, E., Lubich, C. and Roche, M. (1989). The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods, Lecture Notes in Mathematics, Vol. 1409, Springer-Verlag, Berlin.]Search in Google Scholar
[Hairer, E. and Wanner, G. (1991). Solving Ordinary Differential Equations II—Stiff and Differential-Algebraic Problems, Springer-Verlag, Berlin/Heidelberg.10.1007/978-3-662-09947-6]Search in Google Scholar
[Hammersley, J. M. and Handscomb, D. C. (1964). Monte-Carlo Methods, John Wiley & Sons, New York, NY.10.1007/978-94-009-5819-7]Search in Google Scholar
[Hoefkens, J. (2001). Rigorous Numerical Analysis with High-Order Taylor Models, Ph.D. thesis, Michigan State University, East Lansing, MI, Available at: http://www.bt.pa.msu.edu/cgi-bin/display.pl?name=hoefkensphd]Search in Google Scholar
[Iavernaro, F. and Mazzia, F. (1998). Solving ordinary differential equations by generalized Adams methods: Properties and implementation techniques, Applied Numerical Mathematics 28(2): 107-126.10.1016/S0168-9274(98)00039-7]Search in Google Scholar
[Jaulin, L., Kieffer, M., Didrit, O. and Walter, É. (2001). Applied Interval Analysis, Springer-Verlag, London.10.1007/978-1-4471-0249-6]Search in Google Scholar
[Keil, C. (2007). Profil/BIAS, Version 2.0.4, Available at: www.ti3.tu-harburg.de/keil/profil/]Search in Google Scholar
[Krawczyk, R. (1969). Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken, Computing 4(3): 189-201, (in German).10.1007/BF02234767]Search in Google Scholar
[Kunkel, P., Mehrmann, V., Rath, W. and Weickert, J. (1997). GELDA: A Software Package for the Solution of General Linear Differential Algebraic Equations, pp. 115-138, Available at: http://www.math.tu-berlin.de/numerik/mt/NumMat/Software/GELDA/]Search in Google Scholar
[Lin, Y. and Stadtherr, M. A. (2007). Deterministic global optimization for dynamic systems using interval analysis, CD-Proceedings of the 12th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics SCAN 2006, Duisburg, Germany, IEEE Computer Society, Los Alamitos, CA.10.1109/SCAN.2006.14]Search in Google Scholar
[Moore, R. E. (1966). Interval Arithmetic, Prentice-Hall, Englewood Cliffs, New Jersey, NY.]Search in Google Scholar
[Nedialkov, N. S. (2007). Interval tools for ODEs and DAEs, CD-Proceedings of the 12th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics SCAN 2006, Duisburg, Germany, IEEE Computer Society, Los Alamitos, CA.]Search in Google Scholar
[Nedialkov, N. S. and Pryce, J. D. (2008). DAETS—Differential- Algebraic Equations by Taylor Series, Available at: http://www.cas.mcmaster.ca/~nedialk/daets/]Search in Google Scholar
[Petzold, L. (1982). A description of DASSL: A differential/algebraic systems solver, IMACS Transactions on Scientific Computation 1: 65-68.]Search in Google Scholar
[Rauh, A. (2008). Theorie und Anwendung von Intervall-methoden für Analyse und Entwurf robuster und optimaler Regelungen dynamischer Systeme, Fortschritt-Berichte VDI, Reihe 8, Nr. 1148, Ph.D. thesis, University of Ulm, Ulm, (in German).]Search in Google Scholar
[Rauh, A. and Auer, E. (2008). Verified simulation of ODEs and DAEs in ValEncIA-IVP, Proceedings of the 13th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics SCAN 2008, El Paso, TX, USA, (under review).]Search in Google Scholar
[Rauh, A., Auer, E., Freihold, M., Hofer, E. P. and Aschemann, H. (2008). Detection and reduction of overestimation in guaranteed simulations of hamiltonian systems, Proceedings of the 13th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics SCAN 2008, El Paso, TX, USA, (under review).]Search in Google Scholar
[Rauh, A., Auer, E. and Hofer, E. P. (2007a). ValEncIA-IVP: A comparison with other initial value problem solvers, CD-Proceedings of the 12th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics SCAN 2006, Duisburg, Germany, IEEE Computer Society, Los Alamitos, CA.10.1109/SCAN.2006.47]Search in Google Scholar
[Rauh, A., Auer, E., Minisini, J. and Hofer, E. P. (2007b). Extensions of ValEncIA-IVP for reduction of overestimation, for simulation of differential algebraic systems, and for dynamical optimization, Proceedings of the 6th International Congress on Industrial and Applied Mathematics, Minisymposium on Taylor Model Methods and Interval Methods—Applications, PAMM, Zurich, Switzerland, Vol. 7(1), pp. 1023001-1023002.10.1002/pamm.200700022]Search in Google Scholar
[Rauh, A. and Hofer, E. P. (2009). Interval methods for optimal control, in A. Frediani and G. Buttazzo (Eds.), Proceedings of the 47th Workshop on Variational Analysis and Aerospace Engineering 2007, Erice, Italy, Springer-Verlag, New York, NY, pp. 397-418.10.1007/978-0-387-95857-6_22]Search in Google Scholar
[Rauh, A., Minisini, J. and Hofer, E. P. (2009). Towards the development of an interval arithmetic environment for validated computer-aided design and verification of systems in control engineering, Proceedings of the Dagstuhl Seminar 08021: Numerical Validation in Current Hardware Architectures, Dagstuhl, Germany, Lecture Notes in Computer Science, Vol. 5492, Springer-Verlag, Berlin/Heidelberg, pp. 175-188.]Search in Google Scholar
[Röbenack, K. (2002). On the efficient computation of higher order maps adkfg(x) using Taylor arithmetic and the Campbell-Baker-Hausdorff formula, in A. Zinober and D. Owens (Eds.), Nonlinear and Adaptive Control, Lecture Notes in Control and Information Science, Vol. 281, Springer, London, pp. 327-336.]Search in Google Scholar