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Sibirskii Matematicheskii Zhurnal, 2017, Volume 58, Number 4, Pages 761–770
DOI: https://doi.org/10.17377/smzh.2017.58.404 (Mi smj2895) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Solving a variational parabolic equation with the periodic condition by a projection-difference method with the Crank–Nicolson scheme in time

A. S. Bondarev, V. V. Smagin

Voronezh State University, Voronezh, Russia
Full-text PDF (278 kB) Citations (1)
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DOI: https://doi.org/10.17377/smzh.2017.58.404
Abstract: A solution to a smoothly solvable linear variational parabolic equation with the periodic condition is sought in a separable Hilbert space by an approximate projection-difference method using an arbitrary finite-dimensional subspace in space variables and the Crank–Nicolson scheme in time. Solvability, uniqueness, and effective error estimates for approximate solutions are proven. We establish the convergence of approximate solutions to a solution as well as the convergence rate sharp in space variables and time.
Keywords: Hilbert space, parabolic equation, periodic condition, projection-difference method, Crank–Nicolson scheme.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00197
The authors were supported by the Russian Foundation for Basic Research (Grant 16-01-00197).
Received: 11.06.2016
Revised: 12.05.2017
English version:
Siberian Mathematical Journal, 2017, Volume 58, Issue 4, Pages 591–599
DOI: https://doi.org/10.1134/S0037446617040048
Bibliographic databases:
Document Type: Article
UDC: 517.988.8
Language: Russian
Citation: A. S. Bondarev, V. V. Smagin, “Solving a variational parabolic equation with the periodic condition by a projection-difference method with the Crank–Nicolson scheme in time”, Sibirsk. Mat. Zh., 58:4 (2017), 761–770; Siberian Math. J., 58:4 (2017), 591–599
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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