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

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Journal of Siberian Federal University. Mathematics & Physics, 2012, Volume 5, Issue 2, Pages 256–263 (Mi jsfu240)

This article is cited in 4 scientific papers (total in 4 papers)

Stability of multilayer finite difference schemes and amoebas of algebraic hypersurfaces

Marina S. Rogozina

Institute of Mathematics, Siberian Federal University, Krasnoyarsk, Russia

Full-text PDF (172 kB) Citations (4)

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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.

Received: 18.12.2011
Received in revised form: 25.01.2012
Accepted: 10.02.2012

Document Type: Article

UDC: 517.55

Language: Russian

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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https://www.mathnet.ru/eng/jsfu240

https://www.mathnet.ru/eng/jsfu/v5/i2/p256

This publication is cited in the following 4 articles:

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
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
Marina S. Rogozina, “On the correctness of polynomial difference operators”, Zhurn. SFU. Ser. Matem. i fiz., 8:4 (2015), 437–441
M. S. Rogozina, “On the Solvability of the Cauchy Problem for a Polynomial Difference Operator”, J. Math. Sci., 213:6 (2016), 887–896

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Журнал Сибирского федерального университета. Серия "Математика и физика"

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