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Approximation of linear differential-difference equations and its application
Ilika Svitlana Anatolyivna 1 , Tuzyk Iryna Ivanivna 1 , Piddubna Larisa Andriivna 1 , Cherevko Igor Mykhailovych 1
1 Department of Mathematical Modeling, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine
Keywords: linear differential-difference equations, delays, quasi-polynomials, stability of solutions
Abstract
An approximation scheme of systems of linear differential equations with many delays is investigated. We considered its application for the approximated finding of non-asymptotic roots of quasi-polynomials. Also we investigate stability of solutions and coefficient areas of linear differential equations with delays.
References

Salukvadze M. E. To the problem of synthesis of an optimal regulator in linear systems with a delay, subject to constant resistance perturbations // Automatics and telemechanics. - 1962-23, No. 2. - C. 1595-1600.

Repyn Yu. M. Tretiakov V. E. Solution of the problem of analytical construction of a regulator on modeling devices // Automation and telemechanics. - 1963. - T. 24, No. 6. - C. 738-743.

Krasovskyi N.N. On approximation of one task of analytical designing of regulators in a system with delay // PMM. - 1964. - T. 28, No. 4. - C. 716-725.

Matvii O.V., Cherevko I.M. On Approximation of Systems with Restriction and Their Stability // Nonlinear Oscillations. - 2004. - T. 7, No. 2. - P. 208-216.

https://doi.org/10.1007/s11072-005-0006-x

Matvii O.V., Pernai S.A., Cherevko I.M. On the stability of linear systems with the threat // Scientific Newsletter of Chernivtsi University: Sb. sciences works - Chernivtsi: Ruta, 2008. - Vip. 421: Mathematics. - P. 66-70.

Matvii O.V., Pernai S.A., Cherevko I.M. Approximation of non-asymptotic roots of quasipolines of linear differential equations with many problems // Scientific bulletin of Chernivtsi university: Sb. sciences works - Chernivtsi, 2010. - Vip. 501: Mathematics. - P. 69-73.

Klevchuk I.I., Pernai S.A., Cherevko I.M. Construction of regions of stability of linear differential differential equations // Reports of the National Academy of Sciences of Ukraine. - 2012. - №7. - P. 28-34.

Cherevko I.M., Piddubna L.A., Ilika S.A. On the approximation of systems with delay and their stability // International. scientific conf. "Dynamic Systems: Sustainability, Management, Optimization" to the 100th anniversary of the birth of E.A. Barbashin (September 24-29, 2018, Minsk, Belorussia). - Minsk, 2018. - C. 1214.

Repyn Yu. M. On the approximate replacement of systems with delay by ordinary differential equations // PMM. - 1965. - 29, No. 2. - P. 226-245.

Ilika S.A., Matvii O.V., Piddubna L.A., Cherevko I.M. Approximation schemes of differential-functional equations and their application // Bukovinsky Mathematical Journal. - T.2, No. 2-3. - Chernivtsi: Chernivtsi National Park Unt., 2014. - pp. 92-96.

Krasovskyi N. N. Some problems in the theory of motion stability. - M.: Gostekhizdat, 1959. - 212 p.

Elsholts L. E. Introduction to the theory of differential equations with a deflection argument / L. E. Elsgolz, S. B. Norkin. - M.: Science, 1971. - 296 p. 13.

Manyk O. (Ph.D., Cherevko I.M.) Computer simulation of linear differential equations with a delay // Materials of the Student Scientific Conference of the Chernivtsi National University named after Yuri Fedkovich (25-27 April 2017). Mathematical sciences. - Chernivtsi: ChNU, 2017. - P. 39-40.

Khusaynov D. Ya., Yunkova E. A. Estimation of the Delay Value in Linear Differential Systems with Deviating Argument // Ukrainian Mathematical Journal. - 1983 - 35, No. 2. - P. 261-264.

https://doi.org/10.1007/BF01088943

Cite
ACS Style
Ilika, S.A.; Tuzyk, I.I.; Piddubna, L.A.; Cherevko, I.M. Approximation of linear differential-difference equations and its application. Bukovinian Mathematical Journal. 2019, 6 https://doi.org/ https://doi.org/10.31861/bmj2018.03.080
AMA Style
Ilika SA, Tuzyk II, Piddubna LA, Cherevko IM. Approximation of linear differential-difference equations and its application. Bukovinian Mathematical Journal. 2019; 6(3-4). https://doi.org/ https://doi.org/10.31861/bmj2018.03.080
Chicago/Turabian Style
Svitlana Anatolyivna Ilika, Iryna Ivanivna Tuzyk, Larisa Andriivna Piddubna, Igor Mykhailovych Cherevko. 2019. "Approximation of linear differential-difference equations and its application". Bukovinian Mathematical Journal. 6 no. 3-4. https://doi.org/ https://doi.org/10.31861/bmj2018.03.080
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