Abstract
Using the projection-difference method, we construct an approximate solution of an abstract linear parabolic equation in a separable Hilbert space with a periodic condition for a solution. We use the Galerkin method for the spatial variables and the implicit Euler discretization for time. We obtain root mean square estimates of the error of approximate solutions that are effective both in time and spatial variables; these estimates imply the convergence of approximate solutions to an exact solution and allow one to find the convergence rate.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 175, Proceedings of the XVII All-Russian Youth School-Conference “Lobachevsky Readings-2018,” November 23-28, 2018, Kazan. Part 1, 2020.
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Bondarev, A.S. Root Mean Square Error Estimates for the Projection-Difference Method for the Approximate Solution of a Parabolic Equation with a Periodic Condition for the Solution. J Math Sci 272, 866–871 (2023). https://doi.org/10.1007/s10958-023-06478-y
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DOI: https://doi.org/10.1007/s10958-023-06478-y
Keywords and phrases
- Hilbert space
- parabolic equation
- periodic condition
- projection-difference method
- root mean square error estimate