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Abstrakty
The paper presents some improvements of the Lohner's algorithm for the rigorous enclosure of trajectories of an ODE.
Czasopismo
Rocznik
Tom
Strony
9--28
Opis fizyczny
Bibliogr. 9 poz.
Twórcy
autor
- Jagiellonian University, Institute of Mathematics Reymonta 4, 30-059 Kraków, Poland, uikleine@cyf-kr.edu.pl
Bibliografia
- [Lohner]Lohner R.J.: Computation of Guaranteed Endosures for the. Solutions of Ordinary Initital and Boundary Value Problems, in: J.R. Cash. I. Gladwell, (eds.). Computationat Ordinary Differential Equations, Clarendon Press, Oxford 1992.
- [ACSJ Andrade M.Y.A., Comba J.L.D., Stolfi J.; Affine arithmetic (Extended abstract), presented at INTERVAL'94, St. Petersburg (Russia), March 5-10, 1994. Also available at: http://www.ic.unicamp.br/~stolfi/EXPORT/proj ects/affine-arith/.
- [MZ] Mrozek M., Zgliczyński P.; Set arithmetic and the, endosing problem in dynamics, Annales Poi. Math., 2000, pp. 237-259.
- [MNK] Miyata T., Nagamoto Y., Kashiwagi M.; Long Time Integration for Initial Value Problems of Ordinary Differential Equations Using Power Series Arithmetic, IEICE Trans. Fundamentals, Vol. E84-A, 9, 2001, pp. 2230-2237.
- [NJ] Nedialkov N.S., Jackson K.R.; An Intenal Hermite-Obreschkoff Method for Computing Rigorous Bounds on the Solution of an Initial Value Problem for an Ordinary Differential Equation, Reliable Computing, 5, 1999, pp. 289-310 and as a chapter in the book: T. Csende.s, (ed.), Developments in Reliable, Computing, Kluwer, Dordrecht, Netherlands, 1999, pp. 289-310, and http://www.es.toronto.edu/NA/reports.htmltfned.SCAN98.
- [Zgli] Zgliczynski P.; Gl-Lohner algorithm, Foundation of Computational Mathematics, 2, 2002, pp. 429-465.
- [AH] Alefeld G., Herzberger J.; Introduction to Internal Computation, Academic Press, NY 1983.
- [M66] Moore R.E.; Internal Analysis, Prentice Hall, Englewood Cliffs, N.J., 1966.
- [M79J Moore R.E.; Methods and Applications of Internal Analysis, SIAM, Philadelphia 1979.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUJ5-0005-0019