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The root condition for the third order polynomials. (English) Zbl 1014.65065

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
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