Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2023, Volume 221, Pages 115–127
DOI: https://doi.org/10.36535/0233-6723-2023-221-115-127 (Mi into1134) 		 
Difference schemes of the finite element method of increased accuracy for solving nonstationary equations

D. Utebaev, G. Kh. Utepbergenova, M. M. Kazymbetova

Karakalpak State University named after Berdakh
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DOI: https://doi.org/10.36535/0233-6723-2023-221-115-127
Abstract: Based on the finite element method with piecewise-cubic interpolation, we construct and examine three-parameter difference schemes of increased accuracy for a second-order ordinary differential equation. Stability and convergence of difference schemes are proved and accuracy estimates are obtained. The schemes proposed are tested and compared in computing experiments.
Keywords: nonstationary equations, finite difference method, finite element method, difference scheme, stability, convergence, accuracy.
Document Type: Article
UDC: 519.6
MSC: 65N12, 65N30
Language: Russian
Citation: D. Utebaev, G. Kh. Utepbergenova, M. M. Kazymbetova, “Difference schemes of the finite element method of increased accuracy for solving nonstationary equations”, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998).  Moscow, November 1–4, 2021. Part 2, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 221, VINITI, Moscow, 2023, 115–127
Citation in format AMSBIB
\Bibitem{UteUteKaz23}
\by D.~Utebaev, G.~Kh.~Utepbergenova, M.~M.~Kazymbetova
\paper Difference schemes of the finite element method of increased accuracy for solving nonstationary equations
\inbook Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998).  Moscow, November 1–4, 2021. Part 2
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2023
\vol 221
\pages 115--127
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1134}
\crossref{https://doi.org/10.36535/0233-6723-2023-221-115-127}
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