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Vestnik KRAUNC. Fiziko-Matematicheskie Nauki, 2023, Volume 43, Number 2, Pages 87–110
DOI: https://doi.org/10.26117/2079-6641-2023-43-2-87-110
(Mi vkam603)
 

This article is cited in 1 scientific paper (total in 1 paper)

INFORMATION AND COMPUTATION TECHNOLOGIES

Parallelization of a numerical algorithm for solving the Ñauchy problem for a nonlinear differential equation of fractional variable order using OpenMP technology

D. A. Tvyordiyab, R. I. Parovikb, A. R. Hayotovc, A. K. Boltaevc

a Kamchatka State University named after Vitus Bering
b Institute for Cosmophysical Research and Radio Wave Propagation FEB RAS
c V.I. Romanovskiy Institute of Mathematics
References:
Abstract: The article presents a software implementation of a parallel efficient and fast computational algorithm for solving the Cauchy problem for a nonlinear differential equation of a fractional variable order. The computational algorithm is based on a non-local explicit finite-difference scheme, taking into account the approximation of the Gerasimov-Caputo fractional derivative VO included in the main differential equation. The algorithms for parallelization of the non-local explicit finite difference scheme were implemented as functions of the user library of the C programming language using the OpenMP technology. The OpenMP technology allows implementing parallel algorithms for working with the CPU computing node using its multithreading. The C language was chosen because of its versatility and lack of strict restrictions on memory handling. Further in the paper, the efficiency of the parallel algorithm is investigated. Efficiency is understood as the optimal ratio in coordinates: acceleration of calculations – the amount of RAM memory occupied, in comparison with the sequential version of the algorithm. The average computation time is analyzed in terms of: running time, acceleration, efficiency and cost of the algorithm. These algorithms were run on two different computing systems: a gaming laptop and a computing server. For a non-local explicit scheme, a significant performance increase of 3-5 times is shown for various methods of software implementation.
Keywords: fractional derivatives, heredity, memory effect, finite difference schemes, parallel computing, OpenMP.
Funding agency Grant number
Grant of the President of the Russian Federation ÌÄ-758.2022.1.1
The name of the funding programme: This research was funded by grant of the President of the Russian Federation grant number MD-758.2022.1.1 on the topic “Development of mathematical models of fractional dynamics in order to study oscillatory processes and processes with saturation”. Organization that has provided funding: Ministry of Science and Higher Education of the Russian Federation.
Document Type: Article
UDC: 519.642.2, 519.687.1
MSC: Primary 34A08; Secondary 65Y05, 65M06
Language: English
Citation: D. A. Tvyordiy, R. I. Parovik, A. R. Hayotov, A. K. Boltaev, “Parallelization of a numerical algorithm for solving the Ñauchy problem for a nonlinear differential equation of fractional variable order using OpenMP technology”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 43:2 (2023), 87–110
Citation in format AMSBIB
\Bibitem{TvyParHay23}
\by D.~A.~Tvyordiy, R.~I.~Parovik, A.~R.~Hayotov, A.~K.~Boltaev
\paper Parallelization of a numerical algorithm for solving the Ñauchy problem for a nonlinear differential equation of fractional variable order using OpenMP technology
\jour Vestnik KRAUNC. Fiz.-Mat. Nauki
\yr 2023
\vol 43
\issue 2
\pages 87--110
\mathnet{http://mi.mathnet.ru/vkam603}
\crossref{https://doi.org/10.26117/2079-6641-2023-43-2-87-110}
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  • https://www.mathnet.ru/eng/vkam/v43/i2/p87
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Vestnik KRAUNC. Fiziko-Matematicheskie Nauki Vestnik KRAUNC. Fiziko-Matematicheskie Nauki
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