Solving a variational parabolic equation with the periodic condition by a projection-difference method with the Crank–Nicolson scheme in time
- Authors: Bondarev A.S.1, Smagin V.V.1
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Affiliations:
- Voronezh State University
- Issue: Vol 58, No 4 (2017)
- Pages: 591-599
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171288
- DOI: https://doi.org/10.1134/S0037446617040048
- ID: 171288
Cite item
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.
About the authors
A. S. Bondarev
Voronezh State University
Author for correspondence.
Email: obliskuratsiya@bk.ru
Russian Federation, Voronezh
V. V. Smagin
Voronezh State University
Email: obliskuratsiya@bk.ru
Russian Federation, Voronezh