Optimal pruning in parametric differential equations

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2239, Issue , 2001, Pages 539-553

  Janssen, Micha ^a   Van Hentenryck, Pascal ^b   Deville, Yves ^a  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^b BROWN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER PROGRAMMING; CONSTRAINT THEORY; INITIAL VALUE PROBLEMS; NUMERICAL METHODS; OPTIMIZATION; POLYNOMIALS;

CONSTRAINT SATISFACTION; HERMITE INTERPOLATION; INTERVAL METHODS; OPTIMAL EVALUATIONS; OPTIMAL PRUNING; RUNNING TIME; SCIENCE AND ENGINEERING;

ORDINARY DIFFERENTIAL EQUATIONS;

EID: 23044529413     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45578-7_37     Document Type: Conference Paper

References (22)

1. K. E. Atkinson. An introduction to Numerical Analysis. JohnWiley & Sons, 1988.
2. Berz, M. and Makino, K. Verified Integration of ODEs and Flows Using Differential Algebraic Methods on High-Order Taylor Models. Reliable Computing, 4:361-369, 1998.
3. C. Bendsten and O. Stauning: TADIFF, a Flexible C++ Package for Automatic Differentiation Using Taylor Series. Technical Report 1997-x5-94, Technical University of Denmark, April 1997.
4. J. Cruz, and P. Barahona. An Interval Constraint Approach to Handle Parametric Ordinary Differential Equations for Decision Support. EKBD-99, 93-108, 1999.
5. G. F. Corliss and R. Rihm. Validating an a Priori Enclosure Using High-OrderTaylor Series. In Scientific Computing, Computer Arithmetic, and Validated Numerics, 1996.
6. Y. Deville, M. Janssen, and P. Van Hentenryck. Consistency Techniques in Ordinary Differential Equations. In CP’98, Pisa, Italy, October 1998.
7. Eijgenraam, P. The Solution of Initial Value Problems Using Interval Arithmetic. Mathematical Centre Tracts No. 144. Stichting Mathematisch Centrum, Amsterdam, 1981.
8. W. H. Enright, T. E. Hull, and B. Lindberg. Comparing Numerical Methods for Stiff Systems of ODEs. BIT, 15:10-48, 1975.
9. R. D. Grigorieff. Numerik gewöhnlicher Differentialgleichungen 1. Teubner, 1972.
10. E. Hairer, S.P. Nørsett, G. Wanner. Solving Ordinary Differential Equations I. Springer-Verlag, Berlin, 1987.
11. M. Janssen, Y. Deville, and P. Van Hentenryck. Multistep Filtering Operators for Ordinary Differential Equations. In CP’99, Alexandria, VA, October 1999.
12. M. Janssen, P. Van Hentenryck, and Y. Deville A Constraint Satisfaction Approach to Parametric Differential Equations In IJCAI-2001, Seattle, WA, August 2001.
13. O. Knüppel. PROFIL/BIAS - A Fast Interval Library. Computing, 53(3-4), 1994.
14. Krueckeberg, F. Ordinary Differential Equations. In E. Hansen, editor, Topics in Interval Analysis, page 91-97. Clarendon Press, Oxford, 1969.
15. Lohner R. J. Enclosing the Solutions of Ordinary Initial and Boundary Value Problems. In Computer Arithmetic, Wiley, 1987.
16. R.E. Moore. Interval Analysis. Prentice-Hall, Englewood Cliffs, N.J., 1966.
17. N. S. Nedialkov. Computing Rigorous Bounds on the Solution of an Initial Value Problem for an Ordinary Differential Equation, Ph.D. Thesis, Univ. of Toronto, 1999.
18. N.S. Nedialkov and K.R. Jackson. An Interval Hermite-Obreschkoff Method for Computing Rigorous Bounds on the Solution of an Initial Value Problem for an ODE, Developments in Reliable Computing, Kluwer, 1999.
19. L. Perko: Differential Equations and Dynamical Systems. Springer-Verlag, 2000.
20. R. Rihm. Implicit Methods for Enclosing Solutions of ODEs. J. of Universal Computer Science, 4(2), 1998. 1
21. J. Stoer and R. Bulirsch. Introduction to Numerical Analysis. Springer-Verlag, 1980.
22. P. Van Hentenryck, L. Michel, and Y. Deville. Numerica: a Modeling Language for Global Optimization. The MIT Press, Cambridge, Mass., 1997.