GET_pdf delibra

Volume 6 (1) 2000, 41-59


Gajda Karol 1, Marciniak A. 2, Szyszka Barbara 1

1Institute of Mathematics, 2Institute of Computing Science
Poznań University of Technology
Piotrowo 3a, 60-965 Poznań, Poland

DOI:   10.12921/cmst.2000.06.01.41-59



The paper presents three- and four-stage implicit interval methods of Runge-Kutta type and is a continuation of our previous paper [6] dealing with one- and two-stage methods of this kind. It is shown that the exact solution of the initial value problem belongs to interval-solutions obtained by both kinds of these methods (three- and four-stage). We also present some approximations of the widths of interval-solutions.


[1] Butcher, J. C., The Numerical Analysis of Ordinary Differential Equations. Runge-Kutta and General Linear Methods, J. Wiley & Sons, Chichester 1987.
[2] Gajda, K., Marciniak, A., Szyszka, B., Inteiyal Methods of Runge-Kutta Type in Floating-Point Internal Arithmetics. Part II [in Polish], Technical Report RB-028/2000, Poznań University of Technology, Institute of Computing Science, Poznań 2000.
[3] Hairer, E., Nørsett, S. P., Wanner, G., Solving Ordinary Differential Equations I. Nonstiff Problems, Springer-Verlag, Berlin, Heidelberg 1987.
[4] Kalmykov, S. A., Šokin, Ju. I., Juldašev, Z. H., Methods of Inteival Analysis [in Russian], Nauka, Novosibirsk 1986.
[5] Krupowicz, A., Numerical Methods of Initial Value Problems of Ordinary Differential Equations [in Polish], PWN, Warsaw 1986.
[6] Marciniak, A., Szyszka, B., One- and Two-Stage Implicit Inteiyal Methods of Runge-Kutta Type, Computational Methods in Science and Technology 5 (1999), 53-65.
[7] Marciniak, A., Interval Methods of Runge-Kutta Type in Floating-Point Inteiyal Arithmetics [in Polish], Technical Report RB-027/99, Poznań University of Technology, Institute of Computing Science, Poznań 1999.
[8] Marciniak, A., Gajda, K., Marlewski, A., Szyszka, B., The Concept of an Object-Oriented System for Solving the Initial Value Problem by Interval Methods of Runge-Kutta Type [in Polish], Pro Dialog 8 (1999), 39-82.
[9] Marciniak, A., Marlewski, A., Inteiyal Representations of Non-Machine Numbers in Object Pascal [in Polish], Pro Dialog 7 (1998), 75-100.
[10] Šokin, Ju. I., Inteiyal Analysis [in Russian], Nauka, Novosibirsk 1981.