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JOURNALS // Matematicheskoe modelirovanie // Archive

Matem. Mod., 2001 Volume 13, Number 2, Pages 17–26 (Mi mm672)

This article is cited in 4 papers

International Conference on Environmental Mathematical Modeling and Numerical Analysis (Rostov-on-Don)

Monotone difference schemes for equations with mixed derivative

A. A. Samarskiia, V. I. Mazhukina, P. P. Matusb, G. I. Shishkinc

a Institute for Mathematical Modelling, Russian Academy of Sciences
b Institute of Mathematics, National Academy of Sciences of the Republic of Belarus
c Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: There are considered elliptic and parabolic equations of arbitrary dimension with alternating coefficients at mixed derivatives. For such equations monotone difference schemes of the second order of local approximation are constructed. Schemes suggested satisfy the principle of maximum. A priori estimates of stability in the norm $Ñ$ without limitation on the grid steps $\tau$ and $h_\alpha$, $\alpha=l,2,\dots,p$ are obtained (unconditional stability).

Received: 29.10.1999



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