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Polynomial quasisolutions of linear second-order differential-difference equations

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Ukrainian Mathematical Journal Aims and scope

Abstract

We consider the scalar linear second-order differential-difference equation with delay {fx159-01}. This equation is investigated by the method of polynomial quasisolutions based on the representation of an unknown function in the form of a polynomial {ie159-01}. Upon the substitution of this polynomial in the original equation, the residual Δ(t) = O(t N−1) appears. An exact analytic representation of this residual is obtained. We show the close connection between a linear differential-difference equation with variable coefficients and a model equation with constant coefficients, the structure of whose solution is determined by the roots of the characteristic quasipolynomial.

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Authors and Affiliations

  1. Institute of Systems Dynamics and Control Theory, Russian Academy of Sciences, Siberian Branch, Irkutsk, Russia

    V. B. Cherepennikov & P. G. Ermolaeva

Authors
  1. V. B. Cherepennikov
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  2. P. G. Ermolaeva
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 1, pp. 140–152, January, 2008.

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Cherepennikov, V.B., Ermolaeva, P.G. Polynomial quasisolutions of linear second-order differential-difference equations. Ukr Math J 60, 159–175 (2008). https://doi.org/10.1007/s11253-008-0049-0

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  • DOI: https://doi.org/10.1007/s11253-008-0049-0

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