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

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...

Full description

Saved in:
Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 272; no. 6; pp. 866 - 871
Main Author Bondarev, A. S.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 02.06.2023
Springer
Springer Nature B.V
Subjects
Convergence
Estimates
Exact solutions
Galerkin method
Hilbert space
Mathematics
Mathematics and Statistics
65J08
root mean square error estimate
Hilbert space
65M60
parabolic equation
periodic condition
projection-difference method
Online AccessGet full text
ISSN1072-3374
1573-8795
1573-8795
DOI10.1007/s10958-023-06478-y

Cover

More Information
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1072-3374
1573-8795
1573-8795
DOI:10.1007/s10958-023-06478-y