The root condition for polynomial of the second degree and a spectral analysis for three-level finite-difference schemes

Abstract

This paper deals with a root condition for polynomial of the second degree. We propose the root condition criterion for such polynomial wiith complex coefficients. The criterion coincide with well-known Hurwitz criterion in the case of real coefficients. We apply this root condition criterion for some three-level finite-difference schemes for Kuramoto-Tsuzuki equations. We investigate polynomial symmetrical and DuFort-Frankel finite-difference schemes and polynomial for one odd-even scheme. We established spectral (conditionally or non-conditionally) stability for these schemes.