Interval Runge-Kutta Methods with Variable Step Sizes

• Autorzy: Marciniak A. , Szyszka B.

Identyfikatory

DOI

10.12921/cmst.2019.0000006

• Języki publikacji: EN

Abstrakty

EN

In a number of our previous papers we have presented interval versions of Runge-Kutta methods (explicit and implicit) in which the step size was constant. Such an approach has required to choose manually the step size in order to ensure an interval enclosure to the solution with the smallest width. In this paper we propose an algorithm for choosing automatically the step size which guarantees the best (i.e., the tiniest) interval enclosure. This step size is determined with machine accuracy.

Słowa kluczowe

EN

initial value problem; Runge-Kutta method; interval Runge-Kutta method; variable step size; floating-point; interval arithmetic

• Wydawca: Institute of Bioorganic Chemistry Scientific Publishers OWN, Polish Academy of Sciences
• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2019
• Tom: Vol. 25, No. 1
• Strony: 17--29
• Opis fizyczny: Bibliogr. 29 poz., rys.

Twórcy

autor

Marciniak A.

• Institute of Computing Science Poznan University of Technology Piotrowo 2, 60-965 Poznan, Poland
• Department of Computer Science State University of Applied Sciences in Kalisz Poznanska 201-205, 62-800 Kalisz, Poland

autor

Szyszka B.

• Institute of Mathematics Poznan University of Technology Piotrowo 3A, 60-965 Poznan, Poland

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).