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
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.
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.
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
\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/vkam603
https://www.mathnet.ru/eng/vkam/v43/i2/p87
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