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Matematicheskie Zametki, 1968, Volume 4, Issue 6, Pages 621–627
(Mi mzm6781)
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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).
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
Linking options:
https://www.mathnet.ru/eng/mzm6781 https://www.mathnet.ru/eng/mzm/v4/i6/p621
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