Geodesic
Stability of multilayer finite difference schemes and amoebas of algebraic hypersurfaces
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 2, pp. 256-263

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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. 
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     author = {Marina S. Rogozina},
     title = {Stability of multilayer finite difference schemes and amoebas of algebraic hypersurfaces},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {256--263},
     publisher = {mathdoc},
     volume = {5},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2012_5_2_a11/}
}
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Marina S. Rogozina. Stability of multilayer finite difference schemes and amoebas of algebraic hypersurfaces. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 2, pp. 256-263. http://geodesic.mathdoc.fr/item/JSFU_2012_5_2_a11/