The root condition for polynomial of the second order and a spectral stability of finite#x2010;difference schemes for Kuramoto#x2010;Tsuzuki equation

摘要

This paper deals with a root condition for polynomial of the second order. We prove the root criterion for such polynomial with complex coefficients. The criterion coincides with well#x2010;known Hurwitz criterion in the case of real coefficients. We apply this root criterion for several three#x2010;layer finite#x2010;difference schemes for Kuramoto#x2010;Tsuzuki equation. We investigate polynomials for symmetrical and DuFort#x2010;Frankel finite#x2010;difference schemes and polynomial for an odd#x2010;even scheme. We establish spectral (conditional or unconditional) stability for these schemes.