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 Mat. Zametki: Year: Volume: Issue: Page: Find

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

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).

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

Bibliographic databases:

UDC: 518

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
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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
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
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