Abstract
In this paper we consider the initial problem with an initial point for a scalar linear inhomogeneous differential-difference equation of neutral type. For polynomial coefficients in the equation we introduce a formal solution, representing a polynomial of a certain degree (“a polynomial quasisolution”); substituting it in the initial equation, one obtains a residual. The work is dedicated to the definition and the analysis (on the base of numerical experiments) of polynomial quasisolutions for the solutions of the initial problem under consideration.
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References
A. D. Myshkis, Linear Differential Equations with Retarded Argument (Gostekhizdat, Moscow-Leningrad, 1951) [in Russian].
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V. B. Cherepennikov and P. G. Ermolaeva, “Polynomial Quasisolutions of Linear Differential Difference Equations,” Opuscula Math. 26(3), 431–443 (2006).
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Original Russian Text © V.B. Cherepennikov and P.G. Ermolaeva, 2008, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, No. 7, pp. 57–72.
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Cherepennikov, V.B., Ermolaeva, P.G. The numerical experiment in the study of polynomial quasisolutions of linear differential-difference equations. Russ Math. 52, 48–60 (2008). https://doi.org/10.3103/S1066369X08070074
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DOI: https://doi.org/10.3103/S1066369X08070074