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

Abstract

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‐known Hurwitz criterion in the case of real coefficients. We apply this root criterion for several three‐layer finite‐difference schemes for Kuramoto‐Tsuzuki equation. We investigate polynomials for symmetrical and DuFort‐Frankel finite‐difference schemes and polynomial for an odd‐even scheme. We establish spectral (conditional or unconditional) stability for these schemes.

First Published Online: 14 Oct 2010