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J. Sib. Fed. Univ. Math. Phys., 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

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.

Full text: PDF file (172 kB)
References: PDF file   HTML file
UDC: 517.55
Received: 18.12.2011
Received in revised form: 25.01.2012
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
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    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  mathnet  crossref
    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  mathnet  crossref  mathscinet  isi  elib  elib
    3. Marina S. Rogozina, “On the correctness of polynomial difference operators”, Zhurn. SFU. Ser. Matem. i fiz., 8:4 (2015), 437–441  mathnet  crossref
    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  mathnet  crossref
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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