Journal of Siberian Federal University. Mathematics & Physics / Stability of Multilayer Finite Difference Schemes and Amoebas of Algebraic Hypersurfaces

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Issue
Journal of Siberian Federal University. Mathematics & Physics: 2012, Vol. 5, Issue 2
Authors
Rogozina, Marina S.
Contact information
Rogozina, Marina S. : e-mail:
Keywords
difference scheme; Cauchy problem; stability; amoeba of algebraic hypersurfaces
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.

Pages
256-263
Paper at repository of SibFU
http://elib.sfu-kras.ru/handle/2311/2758