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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2019, Volume 59, Number 6, Pages 913–919
DOI: https://doi.org/10.1134/S0044466919060036 (Mi zvmmf10903) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Estimation of the distance between true and numerical solutions

A. K. Alekseeva, A. E. Bondarevb

a Moscow Institute of Physics and Technology, Dolgoprudnyi, Moscow oblast, 141700 Russia
b Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 125047 Russia
Citations (11)
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DOI: https://doi.org/10.1134/S0044466919060036
Abstract: Given an ensemble of numerical solutions generated by different algorithms that are guaranteed to have different errors, the triangle inequality is used to find a neighborhood of a numerical solution that contains the true one. By analyzing the distances between the numerical solutions, the latter can be ranged according to their error magnitudes. Numerical tests for the two-dimensional compressible Euler equations demonstrate the possibility of comparing the errors of different methods and determining a domain containing the true solution.
Key words: computational error, ensemble of numerical solutions, triangle inequality, Euler equations.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00444_а
This work was supported by the Russian Foundation for Basic Research, projects no. 17-01-444A.
Received: 17.07.2017
Revised: 17.07.2017
Accepted: 08.02.2019
English version:
Computational Mathematics and Mathematical Physics, 2019, Volume 59, Issue 6, Pages 857–863
DOI: https://doi.org/10.1134/S0965542519060034
Bibliographic databases:
Document Type: Article
UDC: 519.6
Language: Russian
Citation: A. K. Alekseev, A. E. Bondarev, “Estimation of the distance between true and numerical solutions”, Zh. Vychisl. Mat. Mat. Fiz., 59:6 (2019), 913–919; Comput. Math. Math. Phys., 59:6 (2019), 857–863
Citation in format AMSBIB
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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