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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2023, Volume 63, Number 9, Pages 1438–1445
DOI: https://doi.org/10.31857/S0044466923080173 (Mi zvmmf11612) 		 
General numerical methods

Numerical method for estimating the growth rate of the rounding error in uniform metric

M. I. Zuev, S. I. Serdyukova

Meshcheryakov Laboratory of Information Technologies, Joint Institute for Nuclear Research, 141980, Dubna, Moscow oblast, Russia
DOI: https://doi.org/10.31857/S0044466923080173
Abstract: A numerico-analytical algorithm for estimating the rounding errors in the uniform metric is developed. Their boundedness is established over the entire range of calculating the current-voltage characteristics of long Josephson junctions using the proposed second-order scheme. For a system of two difference equations as an example, it is shown how the growth rate of rounding errors in the uniform metric can be analyzed numerically in the case of a power-law instability. In addition, estimates are obtained for the growth rate of the rounding errors in the uniform metric for the third-order Rusanov scheme. The calculations were carried out on the Govorun supercomputer using the REDUCE system.
Key words: finite-difference methods, estimating the growth of rounding errors in the uniform metric, numerical method, REDUCE system, Govorun supercomputer.
Received: 16.02.2023
Revised: 20.03.2023
Accepted: 28.04.2023
English version:
Computational Mathematics and Mathematical Physics, 2023, Volume 63, Issue 9, Pages 1580–1587
DOI: https://doi.org/10.1134/S0965542523080171
Bibliographic databases:
Document Type: Article
UDC: 517.929
Language: Russian
Citation: M. I. Zuev, S. I. Serdyukova, “Numerical method for estimating the growth rate of the rounding error in uniform metric”, Zh. Vychisl. Mat. Mat. Fiz., 63:9 (2023), 1438–1445; Comput. Math. Math. Phys., 63:9 (2023), 1580–1587
Citation in format AMSBIB
\Bibitem{ZueSer23}
\by M.~I.~Zuev, S.~I.~Serdyukova
\paper Numerical method for estimating the growth rate of the rounding error in uniform metric
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2023
\vol 63
\issue 9
\pages 1438--1445
\mathnet{http://mi.mathnet.ru/zvmmf11612}
\crossref{https://doi.org/10.31857/S0044466923080173}
\elib{https://elibrary.ru/item.asp?id=54313680}
\transl
\jour Comput. Math. Math. Phys.
\yr 2023
\vol 63
\issue 9
\pages 1580--1587
\crossref{https://doi.org/10.1134/S0965542523080171}
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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