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Marciniak, Andrzej, Szyszka, Barbara, Hoffmann, Tomasz. (1400). An interval version of the Kuntzmann-Butcher method for solving the initial value problem. سامانه مدیریت نشریات علمی, 10(1), 44-60. doi: 10.22034/cmde.2020.39203.1720
Andrzej Marciniak; Barbara Szyszka; Tomasz Hoffmann. "An interval version of the Kuntzmann-Butcher method for solving the initial value problem". سامانه مدیریت نشریات علمی, 10, 1, 1400, 44-60. doi: 10.22034/cmde.2020.39203.1720
Marciniak, Andrzej, Szyszka, Barbara, Hoffmann, Tomasz. (1400). 'An interval version of the Kuntzmann-Butcher method for solving the initial value problem', سامانه مدیریت نشریات علمی, 10(1), pp. 44-60. doi: 10.22034/cmde.2020.39203.1720
Marciniak, Andrzej, Szyszka, Barbara, Hoffmann, Tomasz. An interval version of the Kuntzmann-Butcher method for solving the initial value problem. سامانه مدیریت نشریات علمی, 1400; 10(1): 44-60. doi: 10.22034/cmde.2020.39203.1720

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

Computational Methods for Differential Equations
مقاله 4، دوره 10، شماره 1، فروردین 2022، صفحه 44-60    اصل مقاله (169.19 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2020.39203.1720
نویسندگان
Andrzej Marciniak1، 2؛ Barbara Szyszka* 3؛ Tomasz Hoffmann4
1Institute of Computing Science, Poznan University of Technology, Piotrowo 2, 60-965 Poznan, Poland.
2Department of Computer Science, Higher Vocational State School in Kalisz Poznanska 201-205, 62-800 Kalisz, Poland.
3Institute of Mathematics, Poznan University of Technology, Piotrowo 3A, 60-965 Poznan, Poland.
4Poznan Supercomputing and Networking Center, Jana Pawła II 10, 61-139 Poznan, Poland.
چکیده
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.
کلیدواژه‌ها
Initial value problem؛ Runge-Kutta methods؛ Kuntzmann-Butcher method؛ Interval Runge-Kutta methods؛ Floating-point interval arithmetic
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