Условия, при которых корни многочлена лежат внутри единичного круга

Abstract

For solution of differential equations with difference methods required to investi-gate difference scheme on stability. If the modulo of roots of the corresponding linear operator is less than one then the scheme is stability. In the article the problem of finding the conditions under which all modules of the roots of a polynomial is less than one, reduced to Routh-Hurwitz conditions for special polynomial, which is built on the original problem. Coefficient conditions for polynomials of the second and third orders are given. Method is useful when the theoretical study systems, you can specify coefficients change, when storing the property conditioning roots a single circle