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. 
@article{IVM_2008_7_a6,
     author = {V. B. Cherepennikov and P. G. Ermolaeva},
     title = {Numerical experiment in the investigation of polynomial quasisolutions of linear differential-difference equations},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {57--72},
     publisher = {mathdoc},
     number = {7},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2008_7_a6/}
}
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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/