Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zh. Vychisl. Mat. Mat. Fiz.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Zh. Vychisl. Mat. Mat. Fiz., 2012, Volume 52, Number 6, Page 1001 (Mi zvmmf9617)  

This article is cited in 3 scientific papers (total in 3 papers)

A highly accurate homogeneous scheme for solving the laplace equation on a rectangular parallelepiped with boundary values in $C^{k,1}$

E. A. Volkova, A. A. Dosievb

a Steklov Mathematical Institute of the Russian Academy of Sciences
b Eastern Mediterranean University, Department of Applied Mathematics and Computer Science, Famagusta

Abstract: In this paper, a homogeneous scheme with 26-point averaging operator for the solution of Dirichlet problem for LaplaceТs equation on rectangular parallelepiped is analyzed. It is proved that the order of convergence is $O(h^4)$, where $h$ is the mesh step, when the boundary functions are from $C^{3,1}$, and the compatibility condition, which results from the Laplace equation, for the second order derivatives on the adjacent faces is satisfied on the edges. Futhermore, it is proved that the order of convergence is $O(h^6(|{\ln h}|+1))$, when the boundary functions are from $C^{5,1}$, and the compatibility condition for the fourth order derivatives is satisfied. These estimations can be used to justify different versions of domain decomposition methods.

Key words: numerical methods for the 3D Laplace equation, finite difference method, uniform error, domain in the form of rectangular, parallelepiped

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00744
Ministry of Education and Science of the Russian Federation N.Sh-65772.2010.1
Russian Academy of Sciences - Federal Agency for Scientific Organizations
This work was partially supported by the Russian Foundation for Basic Research (project code: 11-01-00744); the program Leading Scientific Schools (project N.Sh-65772.2010.1), and the program Modern Problems in Theoretical Mathematics of the Division of Mathematics, Russian Academy of Sciences.


Full text: PDF file (91 kB)
References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2012, 52:6, 879–886

Bibliographic databases:

UDC: 519.632.4
Received: 28.12.2011
Language:

Citation: E. A. Volkov, A. A. Dosiev, “A highly accurate homogeneous scheme for solving the laplace equation on a rectangular parallelepiped with boundary values in $C^{k,1}$”, Zh. Vychisl. Mat. Mat. Fiz., 52:6 (2012), 1001; Comput. Math. Math. Phys., 52:6 (2012), 879–886

Citation in format AMSBIB
\Bibitem{VolDos12}
\by E.~A.~Volkov, A.~A.~Dosiev
\paper A highly accurate homogeneous scheme for solving the laplace equation on a rectangular parallelepiped with boundary values in $C^{k,1}$
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2012
\vol 52
\issue 6
\pages 1001
\mathnet{http://mi.mathnet.ru/zvmmf9617}
\elib{https://elibrary.ru/item.asp?id=17745727}
\transl
\jour Comput. Math. Math. Phys.
\yr 2012
\vol 52
\issue 6
\pages 879--886
\crossref{https://doi.org/10.1134/S0965542512060152}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000305735100005}
\elib{https://elibrary.ru/item.asp?id=20472756}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84863189765}


Linking options:
  • http://mi.mathnet.ru/eng/zvmmf9617
  • http://mi.mathnet.ru/eng/zvmmf/v52/i6/p1001

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Dosiyev A.A., Sadeghi H.M.-M., “On a highly accurate approximation of the first and pure second derivatives of the Laplace equation in a rectangular parallelpiped”, Adv. Differ. Equ., 2016, 145  crossref  mathscinet  isi  elib  scopus
    2. Dosiyev A.A., Abdussalam A., “On the High Order Convergence of the Difference Solution of Laplace'S Equation in a Rectangular Parallelepiped”, Filomat, 32:3 (2018), 893–901  crossref  mathscinet  isi  scopus
    3. Dosiyev A.A., Sarikaya H., “On the Difference Method For Approximation of Second Order Derivatives of a Solution of Laplace'S Equation in a Rectangular Parallelepiped”, Filomat, 33:2 (2019), 633–643  crossref  mathscinet  isi
  • ∆урнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
    Number of views:
    This page:203
    Full text:65
    References:42
    First page:1

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021