Štikonas, A. The root condition for the third order polynomials. (English) Zbl 1014.65065 Math. Model. Anal. 4, 163-173 (1999). Summary: This paper deals with a root condition for polynomial of the second- and third-order. We prove the root criterion for such polynomial with complex coefficients and find regions for the root condition in the phase space of special coefficients. MSC: 65L20 Stability and convergence of numerical methods for ordinary differential equations 65H05 Numerical computation of solutions to single equations 65L12 Finite difference and finite volume methods for ordinary differential equations 65L05 Numerical methods for initial value problems involving ordinary differential equations 65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems Keywords:stability; consistency; convergence; finite-difference schemes; multistep methods; root condition PDFBibTeX XMLCite \textit{A. Štikonas}, Math. Model. Anal. 4, 163--173 (1999; Zbl 1014.65065)