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 J. Sib. Fed. Univ. Math. Phys., 2012, Volume 5, Issue 2, Pages 256–263 (Mi jsfu240)

Stability of multilayer finite difference schemes and amoebas of algebraic hypersurfaces

Marina S. Rogozina

Institute of Mathematics, Siberian Federal University, Krasnoyarsk, Russia

Abstract: We study the numerical stability of the multilayer finite difference schemes by using methods of the theory of amoebas of algebraic hypersurfaces. We give a necessary condition for the stability of a Cauchy problem for a multilayer scheme and show that it is not a sufficient one. Therefore, we formulate and prove a sufficient condition for the stability.

Keywords: difference scheme, Cauchy problem, stability, amoeba of algebraic hypersurfaces.

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UDC: 517.55
Accepted: 10.02.2012

Citation: Marina S. Rogozina, “Stability of multilayer finite difference schemes and amoebas of algebraic hypersurfaces”, J. Sib. Fed. Univ. Math. Phys., 5:2 (2012), 256–263

Citation in format AMSBIB
\Bibitem{Rog12} \by Marina~S.~Rogozina \paper Stability of multilayer finite difference schemes and amoebas of algebraic hypersurfaces \jour J. Sib. Fed. Univ. Math. Phys. \yr 2012 \vol 5 \issue 2 \pages 256--263 \mathnet{http://mi.mathnet.ru/jsfu240} 

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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. M. S. Rogozina, “On the Solvability of the Cauchy Problem for a Polynomial Difference Operator”, J. Math. Sci., 213:6 (2016), 887–896
2. E. K. Leǐnartas, M. S. Rogozina, “Solvability of the Cauchy problem for a polynomial difference operator and monomial bases for the quotients of a polynomial ring”, Siberian Math. J., 56:1 (2015), 92–100
3. Marina S. Rogozina, “On the correctness of polynomial difference operators”, Zhurn. SFU. Ser. Matem. i fiz., 8:4 (2015), 437–441
4. Marina S. Apanovich, Evgeny K. Leinartas, “Correctness of a two-dimensional Cauchy problem for a polynomial difference operator with constant coefficients”, Zhurn. SFU. Ser. Matem. i fiz., 10:2 (2017), 199–205
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