Stability of Multilayer Finite Difference Schemes and Amoebas of Algebraic Hypersurfaces

Full text (.pdf)
Issue
Математика и физика. Mathematics & Physics. 2012 5 (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