On representations of coefficients in implicit interval methods of Runge - Kutta type

• Autorzy: Marciniak A. , Szyszka B.
• Języki publikacji: EN

Abstrakty

EN

The paper presents one-, two- and three-stage implicit interval methods of Runge-Kutta type for solving the initial value problem. In our previous papers [1] and [2] it was shown that the exact solution belongs to the interval-solution obtained by both kinds of these methods. We continue the problem on the minimization of the widths of interval-solutions.

• Wydawca: Institute of Bioorganic Chemistry Scientific Publishers OWN, Polish Academy of Sciences
• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2004
• Tom: Vol. 10, nr 1
• Strony: 57--71
• Opis fizyczny: Bibliogr. 13 poz., rys.

Twórcy

autor

Marciniak A.

• Poznań University of Technology, Institute of Computing Science Piotrowo 3a, 60-965 Poznań, Poland
• Adam Mickiewicz University, Faculty of Mathematics and Computer Science Umultowska 87, 61-614 Poznań, Poland

autor

Szyszka B.

• Poznań University of Technology, Institute of Mathematics Piotrowo 3a, 60-965 Poznań, Poland

Bibliografia

• [1] A. Marciniak and B. Szyszka, One- and Two-Stage Implicit Interval Methods of Runge-Kutta Type, Computational Methods in Science and Technology 5, OWN, Poznań 1999.
• [2] A. Marciniak, K. Gajda, and B. Szyszka, Three- and Four-Stage Implicit Interval Methodss of Runge-Kutta Type, Computational Methods in Science and Technology 6, OWN, Poznań 2000.
• [3] S. A. Kalmykov, Yu. I. Šokin, and Z. H. Yuldašew, Methodss of Interval Analysis [in Russian], Nauka, Novosibirsk 1986.
• [4] A. Marciniak., K. Gajda, A. Marlewski, and B. Szyszka, The Concept of Object-Oriented System for Solving the Initial Value Problem by Interval Methods of Runge-Kutta Type [in Polish], ProDialog 8, Nakom, Poznań 1999, 39-62.
• [5] A. Marciniak, K. Gajda, and B. Szyszka, Interval Methods of Runge-Kutta Type in Floating-Point Interval Arithmetics [in Polish], Technical Report RB-028/2000, Poznań University of Technology, Institute of Computing Science, Poznań 2000.
• [6] A. Krupowicz, Numerical Methods of Initial Value Problems of Ordinary Differential Equations [in Polish], PWN, Warszawa 1986.
• [7] J. C. Butcher, The Numerical Analysis of Ordinary Differential Equations. Runge-Kutta and General Linear Methods, J. Wiley&Sons, Chichester 1987.
• [8] Yu. I. Šokin, Interval Analysis, [in Russian], Nauka, Novosibirsk 1981.
• [9] J. Kudrewicz., Analizafunkcjonalna dla automatyków i elektroników, Państwowe Wydawnictwo Naukowe, Warszawa 1976.
• [10] A. Marciniak, Finding the Integration Interval for Interval Methods of Runge-Kutta Type in Floating-PointInterval Arithmetics, Pro Dialog 10, Nakom, Poznań 2000, 35-45.
• [11] BorlandDelphi 6. Object Pascal. Language Guide, Borland, Scotts Valley 2001.
• [12] A. Marciniak and A. Marlewski, Interval Representation of Non-Machine Numbers in Object Pascal [in Polish], Pro Dialog 7, Nakom, Poznań 1998, 75-100.
• [13] A. Marciniak and B. Szyszka, Interval Metods of Runge-Kutta Type in Floating-Point Interval Arithmetics [in Polish], Technical Report RB-022/2001, Poznań University of Technology, Institute of Computing Science, Poznań 2001.