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Mat. Zametki, 1968, Volume 4, Issue 6, Pages 621–627 (Mi mz6781)  

This article is cited in 2 scientific papers (total in 2 papers)

On the inevitable error of the method of nets

E. A. Volkov

Steklov Mathematical Institute, USSR Academy of Sciences

Abstract: It is proved that no matter what the solution of an arbitrary boundary-value problem for the two-dimensional Laplace equation, unless it is a special fourth-degree harmonic polynomial, the rate of convergence of the method of square nets using the operator for computation of the four-point arithmetic mean can never be better than $h^2$ (where $h$ is the spacing of the net).

Full text: PDF file (528 kB)

English version:
Mathematical Notes, 1968, 4:6, 865–868

Bibliographic databases:

UDC: 518
Received: 08.05.1968

Citation: E. A. Volkov, “On the inevitable error of the method of nets”, Mat. Zametki, 4:6 (1968), 621–627; Math. Notes, 4:6 (1968), 865–868

Citation in format AMSBIB
\Bibitem{Vol68}
\by E.~A.~Volkov
\paper On the inevitable error of the method of nets
\jour Mat. Zametki
\yr 1968
\vol 4
\issue 6
\pages 621--627
\mathnet{http://mi.mathnet.ru/mz6781}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=250503}
\zmath{https://zbmath.org/?q=an:0185.18601}
\transl
\jour Math. Notes
\yr 1968
\vol 4
\issue 6
\pages 865--868
\crossref{https://doi.org/10.1007/BF01110818}


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    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. E. A. Volkov, “An exponentially convergent method for the solution of Laplace's equation on polygons”, Math. USSR-Sb., 37:3 (1980), 295–325  mathnet  crossref  mathscinet  zmath  isi
    2. E. A. Volkov, “On a combined grid method for solving the Dirichlet problem for the Laplace equation in a rectangular parallelepiped”, Comput. Math. Math. Phys., 47:4 (2007), 638–643  mathnet  crossref  mathscinet  zmath
  • Математические заметки Mathematical Notes
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