Polynomial quasisolutions of linear differential-difference equations

• Autorzy: Cherepennikov V. B. , Ermolaeva P. G.
• Języki publikacji: EN

Abstrakty

EN

The paper discusses a linear differential-difference equation of neutral type with linear coefficients, when at the initial time moment t = 0 the value of the desired function x(t) is known. The authors are not familiar with any results which would state the solvability conditions for the given problem in the class of analytical functions. A polynomial of some degree N is introduced into the investigation. Then the term "polynomial quasisolution" (PQ-solution) is understood in the sense of appearance of the residual Δ(t) = O(tN), when this polynomial is substituted into the initial problem. The paper is devoted to finding PQ-solutions for the initial-value problem under analysis.

Słowa kluczowe

EN

differential-difference equations; neutral type; initial-value problem; polynomial quasisolution

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2006
• Tom: Vol. 26, no. 3
• Strony: 431--443
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Cherepennikov V. B.

autor

Ermolaeva P. G.

• Institute of System Dynamics and Control Theory of Sib. Dep. RAS. Irkutsk, Russia,

Bibliografia

• [1] A.D. Myshkis, Linear differential equations with delayed argument, Gostexizdat, Moscow, 1951 (in Russian).
• [2] E. Pinni, Ordinary differential difference equations, Univ. of Calif. Press., Berkeley and Los Angeles, 1958.
• [3] R. Bellman, K.L. Cooke, Differential difference equations, Academic Press, New York -London, 1963.
• [4] N.V. Azbelev, V.P. Maksimov, L.F. Rakhmatullina, Introduction to the theory of functional differential equations, Nauka, Moscow, 1991 (in Russian).
• [5] V.B. Cherepennikov. Polynomial quasisolutions of linear systems of differential-difference equations. Izv. VUZOV. Mathematics, 1999, N10 - P.49-58.
• [6] G.I. Antoshkina, B. Cherepennikov. Investigation of polynomial quasisolutions of differential-difference equations linear systems based on a mathematical experiment. Optimization, Control, Intellect, Irkutsk, 2000, N5 - P. 15-27.