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An interval version of the Kuntzmann-Butcher method for solving the initial value ‎problem


[ 1 ] Instytut Informatyki, Wydział Informatyki i Telekomunikacji, Politechnika Poznańska | [ 2 ] Instytut Matematyki, Wydział Automatyki, Robotyki i Elektrotechniki, Politechnika Poznańska | [ P ] employee

Scientific discipline (Law 2.0)

[2.3] Information and communication technology

Year of publication


Published in

Computational Methods for Differential Equations

Journal year: 2022 | Journal volume: vol. 10 | Journal number: no. 1

Article type

scientific article

Publication language


  • initial value problem
  • Runge-Kutta methods
  • Kuntzmann-Butcher method
  • interval Runge-Kutta methods
  • floating-point interval arithmetic

EN The Kutzmann-Butcher method is the unique implicit four-stage Runge-Kutta method of order 8. In many problems in ordinary differential equations this method realized in floating-point arithmetic gives quite good approximations to the exact solutions, but the results obtained do not contain any information on rounding errors, representation errors and the error of the method. Thus, we describe an interval version of this method, which realized in floating-point interval arithmetic gives approximations (enclosures in the form of an interval) containing all these errors. The described method can also include data uncertainties in the intervals obtained.

Pages (from - to)

44 - 60




License type

CC BY-NC (attribution - noncommercial)

Open Access Mode

open journal

Open Access Text Version

final published version

Date of Open Access to the publication

at the time of publication

Points of MNiSW / journal


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