The scheme of higher accuracy of approximated dinding of non-asymptotic roots quasipolynomials of linear differential-difference neutral equations is constructed and investigated.

[1] Repin Yu.M. On approximate replacement of systems with delay by ordinary differential equations / / PMM. - 1965. - V. 29, № 2. - P. 226-245.

[2] Piddubna L.A., Cherevko I.M. Approximations of differential-difference equations and calculations of nonasymptotic roots of quasipolynomials // Revue d'analyse numerique et de theorie de l'approximations. - 1999. - Vol. 28, N 1. - P. 15 - 21.

[3] Matviy O.V., Cherevko I.M. On the approximation of systems with delay and their stability // Nonlinear oscillations. - 2004. - T. 7, №2. - P. 2008 -2016.

[4] Matviy O.V., Cherevko I.M. On the approximation of systems of differential-difference equations of neutral type by systems of ordinary differential equations // Nonlinear oscillations. - 2007. - T. 10, №3. - P. 329 - 335.

[5]  Matviy O.V., Pernay S.A., Cherevko I.M. On the stability of linear systems with delay // Nauk. visnyk Chernivtsi un-tu: 3b. nauk. prac Vyp. 421. Mathematics. - Chernivtsi: Ruta, 2008. - P. 66-70.

[6]  Cherevko I.M. Approximation of differential-difference equations and approximation of non-asymptotic roots of quasi-polynomials // Non-linear differential equations and their applications. - K. : Institute of Mathematics of the Academy of Sciences of Ukraine, 1992. - P. 74-84.

[7]  Matviy O.V., Pernay S.A., Cherevko I.M. Approximation of non-asymptotic roots of quasi-polynomials of linear differential equations with many delays / / Nauk. visnyk Chernivtsi un-tu: 3b. nauk. prac Vyp. 501. Mathematics. Chernivtsi: Ruta, 2010. - P. 69-73.

[8] Piddubna L.A., Cherevko I.M. On the approximation of non-asymptotic roots of quasi-polynomials for systems of differential equations of neutral type // Scientific Bulletin of Chernivtsi University: 3b. nauk, pracs Vyp. 191-192. Mathematics. Chernivtsi: Ruta, 2004. - P. 119-122.