Geodesic
Numerical experiment in the investigation of polynomial quasisolutions of linear differential-difference equations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2008), pp. 57-72.

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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.
Keywords: linear differential-difference equations, method of polynomial quasisolutions, numerical experiment. 
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V. B. Cherepennikov; P. G. Ermolaeva. Numerical experiment in the investigation of polynomial quasisolutions of linear differential-difference equations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2008), pp. 57-72. http://geodesic.mathdoc.fr/item/IVM_2008_7_a6/

[1] Myshkis A. D., Lineinye differentsialnye uravneniya s zapazdyvayuschim argumentom, Gostekhizdat, M.–L., 1951, 256 pp.

[2] Pinni E., Obyknovennye differentsialno-raznostnye uravneniya, In. lit., M., 1961, 248 pp. | Zbl

[3] Bellman R., Kuk K., Differentsialno-raznostnye uravneniya, Mir, M., 1967, 548 pp. | Zbl

[4] Cherepennikov V. B., Ermolaeva P. G., “Polynomial quasisolutions of linear differential difference equations”, Opuscula Math., 26/3, Univ. of Gdansk, 2006, 431–443 | MR