Open AccessTHE ROOT CONDITION FOR POLYNOMIAL OF THE SECOND ORDER AND A SPECTRAL STABILITY OF FINITE‐DIFFERENCE SCHEMES FOR KURAMOTO‐TSUZUKI EQUATION
Author(s) -
Artūras Štikonas
Publication year - 1998
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.1998.9637104
Subject(s) - mathematics , polynomial , stability (learning theory) , root (linguistics) , order (exchange) , routh–hurwitz stability criterion , characteristic polynomial , finite difference , mathematical analysis , pure mathematics , linguistics , philosophy , finance , machine learning , computer science , economics
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.