Wrapping Function of the Initial Value Problem for ODE: Applications

Reliable Computing

Volumn 5, Issue 2, 1999, Pages 143-164

  Anguelov, Roumen ^a  

^a VISTA UNIVERSITY   (South Africa)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0013207290     PISSN: 13853139     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1009953406068     Document Type: Article

References (11)

1. Anguelov, R. and Markov, S.: Wrapping Effect and Wrapping Function, Reliable Computing 4 (4) (1998), pp. 311-330.
2. Corliss, G. F.: Where Is Validated ODE Solving Going, in: Herzberger, J. (ed.), Proceedings of the IMACS-GAMM International Symposium on Numerical Methods and Error Bounds, Academie Verlag, Berlin, 1996, pp. 48-57.
3. Eijgenraam, P.: The Solution of Initial Value Problems Using Interval Arithmetic, Mathematical Centre Tracks 144, Mathematisch Centrum, Amsterdam, 1981.
4. Jackson, L.: Interval Arithmetic Error-Bounding Algorithms, SIAM J. Numer. Analysis 12 (1975), pp. 223-238.
5. Lohner, R. J.: Enclosing the Solutions of Ordinary Initial and Boundary Value Problems, in: Kaucher, E. W., Kulisch, U. W., and Ullrich, C. (eds), Computer Arithmetic: Scientific Computation and Programing Languages, Wiley-Teubner Series in Computer Science, Stuttgard, 1987, pp. 255-286.
6. Markov, S.: Isomorphic Embeddings of Abstract Interval Systems, Reliable Computing 3 (3) (1997), pp. 199-207.
7. Moore, R.: Methods and Applications of Interval Analysis, SIAM, Philadelphia, 1979.
8. Nedialkov, N. S., Jackson, K. R., and Corliss, G. F.: Validated Solutions of Initial Value Problems for Ordinary Differential Equations, Technical Report, Computer Science, University of Toronto, 1997.
9. Nickel, K.: How to Fight the Wrapping Effect, in: Interval Mathematics '85, (Lecture Notes in Computer Science 212), Springer, Berlin, 1985, pp. 121-132.
10. Rihm, R.: Interval Methods for Initial Value Problems in ODE, in: Herzberger, J. (ed.), Topics in Validated Computations: Proceedings of the IMACS-GAMM International Workshop on Validated Computations, University of Oldenburg, Elsevier Studies in Computational Mathematics, Elsevier, Amsterdam, New York, 1994.
11. Stetter, H. J.: Algorithms for the Inclusion of Solutions of Ordinary Initial Value Problems, in: Vosmansky, J. and Zlamal, M. (eds), Equadiff 6: Proceedings of the International Conference on Differential Equations and Their Applications (Brno, 1985), (Lecture Notes in Mathematics 1192), Springer-Verlag, Berlin, 1986, pp. 85-94.