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
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.
difference scheme, Cauchy problem, stability, amoeba of algebraic hypersurfaces.
PDF file (172 kB)
Received in revised form: 25.01.2012
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
\paper Stability of multilayer finite difference schemes and amoebas of algebraic hypersurfaces
\jour J. Sib. Fed. Univ. Math. Phys.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
M. S. Rogozina, “On the Solvability of the Cauchy Problem for a Polynomial Difference Operator”, J. Math. Sci., 213:6 (2016), 887–896
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
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
|Number of views:|